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}
}