Accelerated Gradient Methods via Inertial Systems with Hessian-driven Damping
Optimization and Control
2025-02-25 v1
Abstract
We analyze the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system with Hessian-driven damping. We recover a convergence rate, up to a factor of 2 speedup upon Nesterov's scheme, for smooth strongly convex functions. As a byproduct of our analyses, we also derive linear convergence rates for convex functions satisfying quadratic growth condition or Polyak-\L ojasiewicz inequality. As a significant feature of our results, the dependence of the convergence rate on parameters of the inertial system/algorithm is revealed explicitly. This may help one get a better understanding of the acceleration mechanism underlying an inertial algorithm.
Cite
@article{arxiv.2502.16953,
title = {Accelerated Gradient Methods via Inertial Systems with Hessian-driven Damping},
author = {Zepeng Wang and Juan Peypouquet},
journal= {arXiv preprint arXiv:2502.16953},
year = {2025}
}