A successive linear programming algorithm for nonsmooth monotone variational inequalities

被引：6

作者：

Bigi, Giancarlo ^{[1
]}

Panicucci, Barbara ^{[2
]}

机构：

[1] Univ Pisa, Dipartimento Informat, I-56127 Pisa, Italy

[2] Univ Pisa, Dipartimento Matemat Applicata, I-56127 Pisa, Italy

来源：

OPTIMIZATION METHODS & SOFTWARE | 2010年 / 25卷 / 01期

关键词：

variational inequality; monotonicity; cutting plane; Tikhonov regularization; DESCENT METHODS;

D O I：

10.1080/10556780903157885

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

An algorithm for solving nonsmooth monotone variational inequalities subject to linear constraints is proposed. Combining a cutting plane procedure for strictly monotone variational inequalities with the Tikhonov regularization technique, we devise an algorithm based on successive linear programming. Preliminary numerical results are reported.

引用

页码：29 / 35

页数：7

共 16 条

[1] [Anonymous], 2007, Finite-dimensional variational inequalities and complementarity problems
[2] [Anonymous], 1996, Die Grundlehren der mathematischen Wissenschaften
[3] Auslender A., 1976, Optimization Methodes Numeriques
[4] EXISTENCE AND APPROXIMATION OF SOLUTIONS OF NONLINEAR VARIATIONAL INEQUALITIES
BROWDER, FE
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1966, 56 (04) : 1080 - &
[5] AUXILIARY PROBLEM PRINCIPLE EXTENDED TO VARIATIONAL-INEQUALITIES
COHEN, G
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1988, 59 (02) : 325 - 333
[6] EQUIVALENT DIFFERENTIABLE OPTIMIZATION PROBLEMS AND DESCENT METHODS FOR ASYMMETRIC VARIATIONAL INEQUALITY PROBLEMS
FUKUSHIMA, M
[J]. MATHEMATICAL PROGRAMMING, 1992, 53 (01) : 99 - 110
[7] An incremental method for solving convex finite min-max problems
Gaudioso, M
Giallombardo, G
Miglionico, G
[J]. MATHEMATICS OF OPERATIONS RESEARCH, 2006, 31 (01) : 173 - 187
[8] FINITE-DIMENSIONAL VARIATIONAL INEQUALITY AND NONLINEAR COMPLEMENTARITY-PROBLEMS - A SURVEY OF THEORY, ALGORITHMS AND APPLICATIONS
HARKER, PT
PANG, JS
[J]. MATHEMATICAL PROGRAMMING, 1990, 48 (02) : 161 - 220
[9] A proximal bundle method with approximate subgradient linearizations
Kiwiel, KC
[J]. SIAM JOURNAL ON OPTIMIZATION, 2006, 16 (04) : 1007 - 1023
[10] A SEQUENTIAL LINEAR-PROGRAMMING ALGORITHM FOR SOLVING MONOTONE VARIATIONAL-INEQUALITIES
MARCOTTE, P
DUSSAULT, JP
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1989, 27 (06) : 1260 - 1278

← 1 2 →