Solving nonconvex optimization problems via a second order dynamical system with unbounded damping

Abstract

In this paper we study a second order dynamical system with variable coefficients in connection to the minimization problem of a smooth nonconvex function. The convergence of the trajectories generated by the dynamical system to a critical point of the objective function is assured, provided a regularization of the objective function satisfies the Kurdyka-{\L}ojasiewicz property. We also provide convergence rates for the trajectories generated by the dynamical system, formulated in terms of the {\L}ojasiewicz exponent, and we show that the unbounded damping considered in our dynamical system significantly improves the convergence rates known so far in the literature, that is, instead of linear rates we obtain superlinear rates.