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

被引：14
|
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
收藏
页码：1291 / 1318
页数：28
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