# A Concise Lyapunov Analysis of Nesterov's Accelerated Gradient Method

arXiv: https://arxiv.org/abs/2502.17373 · HTML: https://mlsanity.com/paper/2502.17373/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 17 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 7 of 7)

- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights](https://mlsanity.com/paper/1503.01243/) (2015)
- [Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints](https://mlsanity.com/paper/1408.3595/) (2014)
- [Acceleration Methods](https://mlsanity.com/paper/2101.09545/) (2021)
- [On the Convergence of Nesterov's Accelerated Gradient Method in Stochastic Settings](https://mlsanity.com/paper/2002.12414/) (2020)
- [Dissipativity Theory for Nesterov's Accelerated Method](https://mlsanity.com/paper/1706.04381/) (2017)
- [Analysis of Gradient Descent with Varying Step Sizes using Integral Quadratic Constraints](https://mlsanity.com/paper/2210.00644/) (2022)

## Abstract (arXiv)

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.