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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 the method globally convergent and yield the best <inline-formula> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula>-convergence factor. We show that for this family of functions, this convergence factor is superior to the factor obtained from the triple momentum method.

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