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Global Convergence and Asymptotic Optimality of the Heavy Ball Method for a Class of Nonconvex Optimization Problems

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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… Click to show full 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.

Keywords: heavy ball; global convergence; class; convergence; ball method

Journal Title: IEEE Control Systems Letters
Year Published: 2022

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