English

Fast convex optimization via inertial systems with asymptotically vanishing viscosity and Hessian-driven damping

Optimization and Control 2025-07-18 v2

Abstract

We study the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system combining asymptotic vanishing viscous and Hessian-driven damping. We establish a fast sublinear convergence rate in case the objective function is convex and satisfies Polyak-\L ojasiewicz inequality. We also establish a linear convergence rate for strongly convex functions. The results can provide more insights into the convergence property of Nesterov's accelerated gradient method.

Keywords

Cite

@article{arxiv.2506.21730,
  title  = {Fast convex optimization via inertial systems with asymptotically vanishing viscosity and Hessian-driven damping},
  author = {Zepeng Wang and Juan Peypouquet},
  journal= {arXiv preprint arXiv:2506.21730},
  year   = {2025}
}