English

Convergence rates for the Heavy-Ball continuous dynamics for non-convex optimization, under Polyak-\L ojasiewicz condition

Optimization and Control 2022-01-27 v2

Abstract

We study convergence of the trajectories of the Heavy Ball dynamical system, with constant damping coefficient, in the framework of convex and non-convex smooth optimization. By using the Polyak-{\L}ojasiewicz condition, we derive new linear convergence rates for the associated trajectory, in terms of objective function values, without assuming uniqueness of the minimizer.

Keywords

Cite

@article{arxiv.2107.10123,
  title  = {Convergence rates for the Heavy-Ball continuous dynamics for non-convex optimization, under Polyak-\L ojasiewicz condition},
  author = {Vassilis Apidopoulos and Nicolò Ginatta and Silvia Villa},
  journal= {arXiv preprint arXiv:2107.10123},
  year   = {2022}
}