Approaching nonsmooth nonconvex minimization through second order proximal-gradient dynamical systems
Optimization and Control
2017-11-20 v1 Dynamical Systems
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-\L{}ojasiewicz property. We also provide convergence rates for the trajectory formulated in terms of the \L{}ojasiewicz exponent.
Cite
@article{arxiv.1711.06570,
title = {Approaching nonsmooth nonconvex minimization through second order proximal-gradient dynamical systems},
author = {Radu Ioan Bot and Ernö Robert Csetnek and Szilárd Csaba László},
journal= {arXiv preprint arXiv:1711.06570},
year = {2017}
}
Comments
arXiv admin note: text overlap with arXiv:1507.01416, arXiv:1610.00911, arXiv:1703.01339