Convergence rates for the heavy-ball continuous dynamics for non-convex optimization, under Polyak–Łojasiewicz condition

Abstract

We study convergence of the trajectories of the Heavy Ball dynamical system, with constant damping coefficient, in the framework of convex and non-convex smooth optimization. By using the Polyak–Łojasiewicz condition, we derive new linear convergence rates for the associated trajectory, in terms of objective function values, without assuming uniqueness of the minimizer.