Open Problem: Two Riddles in Heavy-Ball Dynamics
Optimization and Control
2025-02-28 v1
Abstract
This short paper presents two open problems on the widely used Polyak's Heavy-Ball algorithm. The first problem is the method's ability to exactly \textit{accelerate} in dimension one exactly. The second question regards the behavior of the method for parameters for which it seems that neither a Lyapunov nor a cycle exists. For both problems, we provide a detailed description of the problem and elements of an answer.
Cite
@article{arxiv.2502.19916,
title = {Open Problem: Two Riddles in Heavy-Ball Dynamics},
author = {Baptiste Goujaud and Adrien Taylor and Aymeric Dieuleveut},
journal= {arXiv preprint arXiv:2502.19916},
year = {2025}
}