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arXiv · 2202.02914

Global convergence and asymptotic optimality of the heavy ball method for a class of non-convex optimization problems

Valery Ugrinovskii·Ian R. Petersen·Iman Shames
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Abstract

In this letter we revisit the famous heavy ball method and study its global convergence for a class of non-convex problems with sector-bounded gradient. We characterize the parameters that render the method globally convergent and yield the best $R$-convergence factor. We show that for this family of functions, this convergence factor is superior to the factor obtained from the triple momentum method.

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Valery Ugrinovskii, Ian R. Petersen, Iman Shames. 2022-02-07. Global convergence and asymptotic optimality of the heavy ball method for a class of non-convex optimization problems. https://arxiv.org/abs/2202.02914

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