English

A Concise Lyapunov Analysis of Nesterov's Accelerated Gradient Method

Optimization and Control 2025-07-08 v3 Machine Learning Systems and Control Systems and Control

Abstract

Convergence analysis of Nesterov's accelerated gradient method has attracted significant attention over the past decades. While extensive work has explored its theoretical properties and elucidated the intuition behind its acceleration, a simple and direct proof of its convergence rates is still lacking. We provide a concise Lyapunov analysis of the convergence rates of Nesterov's accelerated gradient method for both general convex and strongly convex functions.

Keywords

Cite

@article{arxiv.2502.17373,
  title  = {A Concise Lyapunov Analysis of Nesterov's Accelerated Gradient Method},
  author = {Jun Liu},
  journal= {arXiv preprint arXiv:2502.17373},
  year   = {2025}
}

Comments

This update adds a few references to related work

R2 v1 2026-06-28T21:55:52.117Z