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

页码：1291 / 1318

页数：28

共 50 条

[21] On damped second-order gradient systems
Begout, Pascal
Bolte, Jerome
Jendoubi, Mohamed Ali
JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (07) : 3115 - 3143
[22] GRADIENT FLOWS, SECOND-ORDER GRADIENT SYSTEMS AND CONVEXITY
Boulmezaoud, Tahar Z.
Cieutat, Philippe
Daniilidis, Aris
SIAM JOURNAL ON OPTIMIZATION, 2018, 28 (03) : 2049 - 2066
[23] Multiple homoclinic solutions for nonsmooth second-order differential systems
Timoumi, Mohsen
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2024, 43 (1-2): : 113 - 124
[24] Variational methods for nonlinear, nonsmooth second-order periodic systems
Filippakis, M
Papageorgiou, NS
OPTIMIZATION, 2006, 55 (1-2) : 37 - 64
[25] Second-Order Minimization Method for Nonsmooth Functions Allowing Convex Quadratic Approximations of the Augment
M. E. Abbasov
Journal of Optimization Theory and Applications, 2016, 171 : 666 - 674
[26] Second-Order Minimization Method for Nonsmooth Functions Allowing Convex Quadratic Approximations of the Augment
Abbasov, M. E.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2016, 171 (02) : 666 - 674
[27] Involutive distributions and dynamical systems of second-order type
Mestdag, T.
Crampin, M.
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2011, 29 (06) : 747 - 757
[28] Second-order dynamical systems associated to variational inequalities
Bot, Radu Ioan
Csetnek, Erno Robert
APPLICABLE ANALYSIS, 2017, 96 (05) : 799 - 809
[29] Periodic solutions of second-order nonautonomous dynamical systems
Martin Schechter
Boundary Value Problems, 2006
[30] Hinf tracking for a class of second-order dynamical systems
Huang, L.
You, B.
Li, W. L.
ADVANCES IN MECHANICAL ENGINEERING, PTS 1-3, 2011, 52-54 : 589 - 594

← 1 2 3 4 5 →