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arXiv · 2502.19916

Open Problem: Two Riddles in Heavy-Ball Dynamics

Baptiste Goujaud·Adrien Taylor·Aymeric Dieuleveut
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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.

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Baptiste Goujaud, Adrien Taylor, Aymeric Dieuleveut. 2025-02-27. Open Problem: Two Riddles in Heavy-Ball Dynamics. https://arxiv.org/abs/2502.19916

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