Extension to nonconvex equality-constrained optimization

Determine whether an inertial primal-dual dynamical system with implicit Hessian-driven damping can be extended to solve nonconvex optimization problems with linear equality constraints.

Background

The proposed continuous-time and discrete-time methods are analyzed for convex optimization problems, with the principal quantitative results relying on strong convexity in the smooth case and convexity in the nonsmooth extension.

The authors explicitly leave unresolved whether the implicit Hessian-driven primal-dual dynamical-system framework can address nonconvex optimization problems subject to linear equality constraints.

References

Moreover, whether such a dynamical system can be extended to solve non-convex optimization problems with linear equality constraints is also a highly meaningful research direction.

— Inertial Primal-Dual Dynamics Methods Featuring Implicit Hessian-Driven Damping for Convex Optimization Problems in Continuous and Discrete Time  (2608.25519 - Sun et al., 26 Aug 2026) in Section Conclusions