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

被引：16

作者：

Bot, Radu Ioan ^{[1
]}

Csetnek, Ernoe Robert ^{[1
]}

Laszlo, Szilard Csaba ^{[2
]}

机构：

[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[2] Tech Univ Cluj Napoca, Dept Math, Memorandumului 28, Cluj Napoca, Romania

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2018年 / 18卷 / 03期

基金：

奥地利科学基金会;

关键词：

Second-order dynamical system; Nonsmooth nonconvex optimization; Limiting subdifferential; Kurdyka-ojasiewicz property; MAXIMAL MONOTONE-OPERATORS; CONVERGENCE; ALGORITHMS; INCLUSIONS;

D O I：

10.1007/s00028-018-0441-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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-ojasiewicz property. We also provide convergence rates for the trajectory formulated in terms of the ojasiewicz exponent.

引用

页码：1291 / 1318

页数：28

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