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Achieving violation-free distributed optimization under coupling constraints (2404.07609v1)

Published 11 Apr 2024 in math.OC, cs.SY, and eess.SY

Abstract: Constraint satisfaction is a critical component in a wide range of engineering applications, including but not limited to safe multi-agent control and economic dispatch in power systems. This study explores violation-free distributed optimization techniques for problems characterized by separable objective functions and coupling constraints. First, we incorporate auxiliary decision variables together with a network-dependent linear mapping to each coupling constraint. For the reformulated problem, we show that the projection of its feasible set onto the space of primal variables is identical to that of the original problem, which is the key to achieving all-time constraint satisfaction. Upon treating the reformulated problem as a min-min optimization problem with respect to auxiliary and primal variables, we demonstrate that the gradients in the outer minimization problem have a locally computable closed-form. Then, two violation-free distributed optimization algorithms are developed and their convergence under reasonable assumptions is analyzed. Finally, the proposed algorithm is applied to implement a control barrier function based controller in a distributed manner, and the results verify its effectiveness.

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References (31)
  1. A proximal diffusion strategy for multiagent optimization with sparse affine constraints. IEEE Transactions on Automatic Control, 65(11):4554–4567, 2019.
  2. Control barrier function based quadratic programs for safety critical systems. IEEE Transactions on Automatic Control, 62(8):3861–3876, 2016.
  3. Amir Beck. First-Order Methods in Optimization. SIAM, 2017.
  4. Dimitri Bertsekas. Nonlinear Programming. Athena Scientific, 2016.
  5. Fastest mixing markov chain on a graph. SIAM review, 46(4):667–689, 2004.
  6. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends® in Machine learning, 3(1):1–122, 2011.
  7. Convex Optimization. Cambridge university press, 2004.
  8. Distributed constraint-coupled optimization via primal decomposition over random time-varying graphs. Automatica, 131:109739, 2021.
  9. On acceleration with noise-corrupted gradients. In International Conference on Machine Learning, pages 1019–1028. PMLR, 2018.
  10. Distributed anytime-feasible resource allocation subject to heterogeneous time-varying delays. IEEE Open Journal of Control Systems, 1:255–267, 2022.
  11. Dual decomposition for multi-agent distributed optimization with coupling constraints. Automatica, 84:149–158, 2017.
  12. Finite dimensional convexity and optimization, volume 13. Springer Science & Business Media, 2001.
  13. Krisorn Jittorntrum. Sequential algorithms in nonlinear programming. The Australian National University (Australia), 1978.
  14. Jerzy Kyparisis. On uniqueness of kuhn-tucker multipliers in nonlinear programming. Mathematical Programming, 32:242–246, 1985.
  15. Distributed proximal algorithms for multiagent optimization with coupled inequality constraints. IEEE Transactions on Automatic Control, 66(3):1223–1230, 2020.
  16. A unitary distributed subgradient method for multi-agent optimization with different coupling sources. Automatica, 114:108834, 2020.
  17. Inverses of 2×\times× 2 block matrices. Computers & Mathematics with Applications, 43(1-2):119–129, 2002.
  18. Distributed saddle-point subgradient algorithms with laplacian averaging. IEEE Transactions on Automatic Control, 62(6):2720–2735, 2016.
  19. Graph theoretic methods in multiagent networks. Princeton University Press, 2010.
  20. Approximate primal solutions and rate analysis for dual subgradient methods. SIAM Journal on Optimization, 19(4):1757–1780, 2009.
  21. Constraint-coupled distributed optimization: a relaxation and duality approach. IEEE Transactions on Control of Network Systems, 7(1):483–492, 2019.
  22. Extra: An exact first-order algorithm for decentralized consensus optimization. SIAM Journal on Optimization, 25(2):944–966, 2015.
  23. Quantitative sensitivity bounds for nonlinear programming and time-varying optimization. IEEE Transactions on Automatic Control, 67(6):2829–2842, 2021.
  24. Distributed implementation of control barrier functions for multi-agent systems. IEEE Control Systems Letters, 6:1879–1884, 2021.
  25. Safe dual gradient method for network utility maximization problems. In 2022 IEEE 61st Conference on Decision and Control (CDC), pages 6953–6959. IEEE, 2022.
  26. Distributed control design and safety verification for multi-agent systems. arXiv preprint arXiv:2303.12610, 2023.
  27. A new family of feasible methods for distributed resource allocation. In 2021 60th IEEE Conference on Decision and Control (CDC), pages 3355–3360. IEEE, 2021.
  28. Distributed safe resource allocation using barrier functions. Automatica, 153:111051, 2023.
  29. Robustness of control barrier functions for safety critical control. IFAC-PapersOnLine, 48(27):54–61, 2015.
  30. Consensus based approach for economic dispatch problem in a smart grid. IEEE Transactions on Power Systems, 28(4):4416–4426, 2013.
  31. Deep leakage from gradients. Advances in neural information processing systems, 32, 2019.
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