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arXiv · 1711.06570

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

Radu Ioan Bot·Ernö Robert Csetnek·Szilárd Csaba László
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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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Radu Ioan Bot, Ernö Robert Csetnek, Szilárd Csaba László. 2017-11-16. Approaching nonsmooth nonconvex minimization through second order proximal-gradient dynamical systems. https://arxiv.org/abs/1711.06570

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