2000 character limit reached
Convergence proof for first-order position-based dynamics: An efficient scheme for inequality constrained ODEs (2310.01215v2)
Published 2 Oct 2023 in math.NA and cs.NA
Abstract: NVIDIA researchers have pioneered an explicit method, position-based dynamics (PBD), for simulating systems with contact forces, gaining widespread use in computer graphics and animation. While the method yields visually compelling real-time simulations with surprising numerical stability, its scientific validity has been questioned due to a lack of rigorous analysis. In this paper, we introduce a new mathematical convergence analysis specifically tailored for PBD applied to first-order dynamics. Utilizing newly derived bounds for projections onto uniformly prox-regular sets, our proof extends classical compactness arguments. Our work paves the way for the reliable application of PBD in various scientific and engineering fields, including particle simulations with volume exclusion, agent-based models in mathematical biology or inequality-constrained gradient-flow models.
- Acary, V., Brogliato, B.: Numerical Methods for Nonsmooth Dynamical Systems. Applications in Mechanics and Electronics. Lect. Notes Appl. Comput. Mech., vol. 35. Springer, Berlin (2008) Moreau [1977] Moreau, J.J.: Evolution problem associated with a moving convex set in a Hilbert space. Journal of Differential Equations 26(3), 347–374 (1977) https://doi.org/10.1016/0022-0396(77)90085-7 . Accessed 2022-12-07 Filippov [1988] Filippov, A.F.: Differential Equations with Discontinuous Right-hand Sides. Ed. by F. M. Arscott. Transl. from The Russian. Math. Appl., Sov. Ser., vol. 18. Kluwer Academic Publishers, Dordrecht etc. (1988) Brogliato and Tanwani [2020] Brogliato, B., Tanwani, A.: Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability. SIAM Review 62(1), 3–129 (2020) https://doi.org/10.1137/18M1234795 . Accessed 2022-07-12 Braun et al. [2021] Braun, P., Grüne, L., Kellett, C.M.: (In-)Stability of Differential Inclusions: Notions, Equivalences, and Lyapunov-like Characterizations. SpringerBriefs in Mathematics. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-76317-6 . https://link.springer.com/10.1007/978-3-030-76317-6 Accessed 2023-08-19 Kleinert and Simeon [2022] Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Evolution problem associated with a moving convex set in a Hilbert space. Journal of Differential Equations 26(3), 347–374 (1977) https://doi.org/10.1016/0022-0396(77)90085-7 . Accessed 2022-12-07 Filippov [1988] Filippov, A.F.: Differential Equations with Discontinuous Right-hand Sides. Ed. by F. M. Arscott. Transl. from The Russian. Math. Appl., Sov. Ser., vol. 18. Kluwer Academic Publishers, Dordrecht etc. (1988) Brogliato and Tanwani [2020] Brogliato, B., Tanwani, A.: Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability. SIAM Review 62(1), 3–129 (2020) https://doi.org/10.1137/18M1234795 . Accessed 2022-07-12 Braun et al. [2021] Braun, P., Grüne, L., Kellett, C.M.: (In-)Stability of Differential Inclusions: Notions, Equivalences, and Lyapunov-like Characterizations. SpringerBriefs in Mathematics. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-76317-6 . https://link.springer.com/10.1007/978-3-030-76317-6 Accessed 2023-08-19 Kleinert and Simeon [2022] Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Filippov, A.F.: Differential Equations with Discontinuous Right-hand Sides. Ed. by F. M. Arscott. Transl. from The Russian. Math. Appl., Sov. Ser., vol. 18. Kluwer Academic Publishers, Dordrecht etc. (1988) Brogliato and Tanwani [2020] Brogliato, B., Tanwani, A.: Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability. SIAM Review 62(1), 3–129 (2020) https://doi.org/10.1137/18M1234795 . Accessed 2022-07-12 Braun et al. [2021] Braun, P., Grüne, L., Kellett, C.M.: (In-)Stability of Differential Inclusions: Notions, Equivalences, and Lyapunov-like Characterizations. SpringerBriefs in Mathematics. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-76317-6 . https://link.springer.com/10.1007/978-3-030-76317-6 Accessed 2023-08-19 Kleinert and Simeon [2022] Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. 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Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. 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Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Tanwani, A.: Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability. SIAM Review 62(1), 3–129 (2020) https://doi.org/10.1137/18M1234795 . Accessed 2022-07-12 Braun et al. [2021] Braun, P., Grüne, L., Kellett, C.M.: (In-)Stability of Differential Inclusions: Notions, Equivalences, and Lyapunov-like Characterizations. SpringerBriefs in Mathematics. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-76317-6 . https://link.springer.com/10.1007/978-3-030-76317-6 Accessed 2023-08-19 Kleinert and Simeon [2022] Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Braun, P., Grüne, L., Kellett, C.M.: (In-)Stability of Differential Inclusions: Notions, Equivalences, and Lyapunov-like Characterizations. SpringerBriefs in Mathematics. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-76317-6 . https://link.springer.com/10.1007/978-3-030-76317-6 Accessed 2023-08-19 Kleinert and Simeon [2022] Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . 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SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. 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Springer, Cham (2021). https://doi.org/10.1007/978-3-030-76317-6 . https://link.springer.com/10.1007/978-3-030-76317-6 Accessed 2023-08-19 Kleinert and Simeon [2022] Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. 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Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. 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Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Tanwani, A.: Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability. SIAM Review 62(1), 3–129 (2020) https://doi.org/10.1137/18M1234795 . Accessed 2022-07-12 Braun et al. [2021] Braun, P., Grüne, L., Kellett, C.M.: (In-)Stability of Differential Inclusions: Notions, Equivalences, and Lyapunov-like Characterizations. SpringerBriefs in Mathematics. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-76317-6 . https://link.springer.com/10.1007/978-3-030-76317-6 Accessed 2023-08-19 Kleinert and Simeon [2022] Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Braun, P., Grüne, L., Kellett, C.M.: (In-)Stability of Differential Inclusions: Notions, Equivalences, and Lyapunov-like Characterizations. SpringerBriefs in Mathematics. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-76317-6 . https://link.springer.com/10.1007/978-3-030-76317-6 Accessed 2023-08-19 Kleinert and Simeon [2022] Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . 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SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. 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[2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Tanwani, A.: Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability. SIAM Review 62(1), 3–129 (2020) https://doi.org/10.1137/18M1234795 . Accessed 2022-07-12 Braun et al. [2021] Braun, P., Grüne, L., Kellett, C.M.: (In-)Stability of Differential Inclusions: Notions, Equivalences, and Lyapunov-like Characterizations. SpringerBriefs in Mathematics. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-76317-6 . https://link.springer.com/10.1007/978-3-030-76317-6 Accessed 2023-08-19 Kleinert and Simeon [2022] Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Braun, P., Grüne, L., Kellett, C.M.: (In-)Stability of Differential Inclusions: Notions, Equivalences, and Lyapunov-like Characterizations. SpringerBriefs in Mathematics. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-76317-6 . https://link.springer.com/10.1007/978-3-030-76317-6 Accessed 2023-08-19 Kleinert and Simeon [2022] Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. 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Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. 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Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . 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[2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. 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Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Kleinert, J., Simeon, B.: Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems, pp. 73–132. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96173-2_4 . https://doi.org/10.1007/978-3-030-96173-2_4 Accessed 2022-04-05 Buttenschön and Edelstein-Keshet [2020] Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . 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[2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . 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[2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Buttenschön, A., Edelstein-Keshet, L.: Bridging from single to collective cell migration: A review of models and links to experiments. PLOS Computational Biology 16(12), 1008411 (2020) https://doi.org/10.1371/journal.pcbi.1008411 . Accessed 2022-09-26 Maury and Faure [2019] Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. 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[2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . 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[2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . 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[2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. 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Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Maury, B., Faure, S.: Crowds in Equations. An Introduction to the Microscopic Modeling of Crowds. Adv. Textb. Math. World Scientific, Hackensack, NJ (2019). https://doi.org/10.1142/q0163 Dubois et al. [2018] Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. 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Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. 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Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dubois, F., Acary, V., Jean, M.: The Contact Dynamics method: A nonsmooth story. Comptes Rendus Mécanique 346(3), 247–262 (2018) https://doi.org/10.1016/j.crme.2017.12.009 . Accessed 2022-04-05 Brogliato et al. [2002] Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Dam, A., Paoli, L., Ge´not, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Applied Mechanics Reviews 55(2), 107–150 (2002) https://doi.org/10.1115/1.1454112 . Accessed 2023-06-13 Schindler and Acary [2014] Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. 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Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. 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[2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. 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[2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
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[2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Schindler, T., Acary, V.: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook. Mathematics and Computers in Simulation 95, 180–199 (2014) https://doi.org/10.1016/j.matcom.2012.04.012 . Accessed 2023-05-29 Müller et al. [2006] Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. 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Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position Based Dynamics (2006) https://doi.org/10.2312/PE/vriphys/vriphys06/071-080 . Accessed 2022-07-08 Bender et al. [2017] Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . 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Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. 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Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bender, J., Müller, M., Macklin, M.: A Survey on Position Based Dynamics (2017) https://doi.org/10.2312/egt.20171034 . Accessed 2022-07-09 Macklin et al. [2016] Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N.: XPBD: position-based simulation of compliant constrained dynamics. In: Proceedings of the 9th International Conference on Motion In Games. MIG ’16, pp. 49–54. Association for Computing Machinery, New York, NY, USA (2016). https://doi.org/10.1145/2994258.2994272 . https://doi.org/10.1145/2994258.2994272 Accessed 2022-07-08 Macklin et al. [2019] Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . 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International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. 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Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Storey, K., Lu, M., Terdiman, P., Chentanez, N., Jeschke, S., Müller, M.: Small steps in physics simulation. In: Proceedings of the 18th Annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation. SCA ’19, pp. 1–7. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3309486.3340247 . https://doi.org/10.1145/3309486.3340247 Accessed 2022-06-03 Macklin and Müller [2013] Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. 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Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M.: Position based fluids. ACM Transactions on Graphics 32(4), 104–110412 (2013) https://doi.org/10.1145/2461912.2461984 . Accessed 2023-08-19 Macklin et al. [2014] Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Macklin, M., Müller, M., Chentanez, N., Kim, T.-Y.: Unified particle physics for real-time applications. ACM Transactions on Graphics 33(4), 153–115312 (2014) https://doi.org/10.1145/2601097.2601152 . Accessed 2023-08-07 Müller et al. [2020] Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. 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[2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. 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[2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Müller, M., Macklin, M., Chentanez, N., Jeschke, S., Kim, T.-Y.: Detailed Rigid Body Simulation with Extended Position Based Dynamics. Computer Graphics Forum 39(8), 101–112 (2020) https://doi.org/10.1111/cgf.14105 . Accessed 2023-08-19 NVIDIA [2018] NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. 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Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . 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[2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- NVIDIA: PhysX 5.0 SDK (2018). https://developer.nvidia.com/physx-sdk Accessed 2023-08-07 NVIDIA [2020] NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 NVIDIA: Develop on NVIDIA Omniverse Platform (2020). https://developer.nvidia.com/omniverse Accessed 2023-08-07 Camara et al. [2016] Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
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Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Camara, M., Mayer, E., Darzi, A., Pratt, P.: Soft tissue deformation for surgical simulation: a position-based dynamics approach. International Journal of Computer Assisted Radiology and Surgery 11(6), 919–928 (2016) https://doi.org/10.1007/s11548-016-1373-8 . Accessed 2023-08-07 Weiss et al. [2017] Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. 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Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . 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[2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. 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Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Weiss, T., Litteneker, A., Jiang, C., Terzopoulos, D.: Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper). Proceedings of the Tenth International Conference on Motion in Games, 1–8 (2017) https://doi.org/10.1145/3136457.3136462 . arXiv: 1802.02673. Accessed 2022-03-20 Frâncu and Moldoveanu [2017] Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Frâncu, M., Moldoveanu, F.: Position based simulation of solids with accurate contact handling. Computers & Graphics 69, 12–23 (2017) https://doi.org/10.1016/j.cag.2017.09.004 . Accessed 2023-05-31 Pécol et al. [2011] Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. 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[2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
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[2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Pécol, P., Dal Pont, S., Erlicher, S., Argoul, P.: Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations. Annals of Solid and Structural Mechanics 2(2), 69–85 (2011) https://doi.org/10.1007/s12356-011-0019-3 . Accessed 2023-08-08 Monji-Azad et al. [2023] Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. 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Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. 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SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. 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[2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
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Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Monji-Azad, S., Kinz, M., Hesser, J., Löw, N.: SimTool: A toolset for soft body simulation using Flex and Unreal Engine. Software Impacts 17, 100521 (2023) https://doi.org/10.1016/j.simpa.2023.100521 . Accessed 2023-08-07 Brogliato et al. [2006] Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
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[2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. 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[2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Brogliato, B., Daniilidis, A., Lemaréchal, C., Acary, V.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems & Control Letters 55(1), 45–51 (2006) https://doi.org/10.1016/j.sysconle.2005.04.015 . Accessed 2022-04-05 Deuflhard and Röblitz [2015] Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. 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Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Deuflhard, P., Röblitz, S.: A Guide to Numerical Modelling in Systems Biology. Texts Comput. Sci. Eng., vol. 12. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20059-0 Moreau [1999] Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Moreau, J.J.: Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering 177(3), 329–349 (1999) https://doi.org/10.1016/S0045-7825(98)00387-9 . Accessed 2022-11-29 Wu et al. [2020] Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wu, S.-L., Zhou, T., Chen, X.: A Gauss–Seidel Type Method for Dynamic Nonlinear Complementarity Problems. SIAM Journal on Control and Optimization 58(6), 3389–3412 (2020) https://doi.org/10.1137/19M1268884 . Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. 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Accessed 2023-06-23 Edmond and Thibault [2006] Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. 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SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). 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Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
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Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. Journal of Differential Equations 226(1), 135–179 (2006) https://doi.org/10.1016/j.jde.2005.12.005 . Accessed 2022-10-09 Adly et al. [2016] Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. 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[2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. 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Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Adly, S., Nacry, F., Thibault, L.: Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization 26(1), 448–473 (2016) https://doi.org/10.1137/15M1032739 . Accessed 2023-06-06 Luke [2008] Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Luke, D.R.: Finding Best Approximation Pairs Relative to a Convex and Prox-Regular Set in a Hilbert Space. SIAM Journal on Optimization 19(2), 714–739 (2008) https://doi.org/10.1137/070681399 . Accessed 2023-06-06 Lewis et al. [2009] Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9(4), 485–513 (2009) https://doi.org/10.1007/s10208-008-9036-y . Accessed 2022-12-06 Ye et al. [2021] Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Ye, J.J., Yuan, X., Zeng, S., Zhang, J.: Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems. Set-Valued and Variational Analysis 29(4), 803–837 (2021) https://doi.org/10.1007/s11228-021-00591-3 . Accessed 2023-06-29 Bernicot and Venel [2010] Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Bernicot, F., Venel, J.: Differential inclusions with proximal normal cones in Banach spaces. Journal of Convex Analysis 17(2), 451–484 (2010). Accessed 2022-06-01 Venel [2011] Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Venel, J.: A numerical scheme for a class of sweeping processes. Numerische Mathematik 118(2), 367–400 (2011) https://doi.org/10.1007/s00211-010-0329-0 . Accessed 2022-04-05 Bernard et al. [2011] Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). Accessed 2023-06-06 Rockafellar and Wets [1998] Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Bernard, F., Thibault, L., Zlateva, N.: Prox-Regular Sets and Epigraphs in Uniformly Convex Banach Spaces: Various Regularities and Other Properties. Transactions of the American Mathematical Society 363(4), 2211–2247 (2011). 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Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. 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Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
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ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. 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Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. 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Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. 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SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. 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SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. 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SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. 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SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. 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- Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren Math. Wiss., vol. 317. Springer, Berlin (1998). https://doi.org/10.1007/978-3-642-02431-3 Thibault [2022] Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. 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[2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Thibault, L.: Unilateral Variational Analysis in Banach Spaces. In 2 Parts. Part I: General Theory. Part II: Special Classes of Functions And sets (to appear). World Scientific, Singapore (2022). https://doi.org/10.1142/12797 Adly et al. [2017] Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
- Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets. ESAIM: Control, Optimisation and Calculus of Variations 23(4), 1293–1329 (2017) https://doi.org/10.1051/cocv/2016053 . Accessed 2022-10-07 Dontchev and Rockafellar [2014] Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. A View from Variational Analysis, 2nd updated ed. edn. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY (2014). https://doi.org/10.1007/978-1-4939-1037-3 Hesse and Luke [2013] Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Hesse, R., Luke, D.R.: Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems. SIAM Journal on Optimization 23(4), 2397–2419 (2013) https://doi.org/10.1137/120902653 https://doi.org/10.1137/120902653 Wang [2015] Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Wang, H.: A chebyshev semi-iterative approach for accelerating projective and position-based dynamics. ACM Transactions on Graphics 34(6), 246–12469 (2015) https://doi.org/10.1145/2816795.2818063 . Accessed 2023-05-31 Chen et al. [2023] Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Chen, Y., Han, Y., Chen, J., Teran, J.: Position-Based Nonlinear Gauss-Seidel for Quasistatic Hyperelasticity. arXiv:2306.09021 [cs] (2023). https://doi.org/10.48550/arXiv.2306.09021 . http://arxiv.org/abs/2306.09021 Accessed 2023-06-20 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger [2023] Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Acary, Vincent and Bremond, Maurice and Huber, Olivier and Perignon, Franck and Pissard-Gibollet, Roger: Siconos (2023). {https://hal.science/hal-04056972} Brezis [2011] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7 Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York, NY (2011). https://doi.org/10.1007/978-0-387-70914-7
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