Approaching nonsmooth nonconvex minimization through second order proximal-gradient dynamical systems

2017/11/16 by Bot, Radu Ioan, Csetnek, Ernö Robert, László, Szilárd Csaba · 1 citation
#34G25 #47H05 #47J25 #65K10 #90C26 #90C30 #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1711.06570

Abstract

We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system of proximal-gradient type stated in connection with the minimization of the sum of a nonsmooth convex and a (possibly nonconvex) smooth function. The convergence of the generated trajectory to a critical point of the objective is ensured provided a regularization of the objective function satisfies the Kurdyka-Łojasiewicz property. We also provide convergence rates for the trajectory formulated in terms of the Łojasiewicz exponent.

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