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

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