  Among first order optimization methods, Polyak's heavy ball method has long
been known to guarantee the asymptotic rate of convergence matching Nesterov's
lower bound for functions defined in an infinite-dimensional space. In this
paper, we use results on the robust gain margin of linear uncertain feedback
control systems to show that the heavy ball method is provably worst-case
asymptotically optimal when applied to quadratic functions in a finite
dimensional space.
