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Among first order optimization methods, Polyak's heavy ball method has longbeen known to guarantee the asymptotic rate of convergence matching Nesterov'slower bound for functions defined in an infinite-dimensional space. In thispaper, we use results on the robust gain margin of linear uncertain feedbackcontrol systems to show that the heavy ball method is provably worst-caseasymptotically optimal when applied to quadratic functions in a finitedimensional space.

A Robust Control Approach to Asymptotic Optimality of the Heavy Ball Method for Optimization of Quadratic Functions