Some proximal algorithms for linearly constrained general variational inequalities

被引：0

作者：

Li, M. ^{[2
]}

Yuan, X. M. ^{[1
]}

机构：

[1] Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China

[2] Southeast Univ, Sch Econ & Management, Nanjing 210096, Jiangsu, Peoples R China

来源：

OPTIMIZATION | 2012年 / 61卷 / 05期

关键词：

general variational inequality; linear constraint; proximal point algorithm; inexact methods; PROJECTION; CONVERGENCE; EQUILIBRIUM;

D O I：

10.1080/02331934.2010.522714

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

Based on the classical proximal point algorithm (PPA), some PPA-based numerical algorithms for general variational inequalities (GVIs) have been developed recently. Inspired by these algorithms, in this article we propose some proximal algorithms for solving linearly constrained GVIs (LCGVIs). The resulted subproblems are regularized proximally, and they are allowed to be solved either exactly or approximately.

引用

页码：505 / 524

页数：20

共 33 条

[1]

[Anonymous], 2007, Finite-dimensional variational inequalities and complementarity problems

[2]

[Anonymous], 1971, Mathematical Programming

[3] The system of generalized vector equilibrium problems with applications [J].

Ansari, QH ;

Schaible, S ;

Yao, JC .

JOURNAL OF GLOBAL OPTIMIZATION, 2002, 22 (1-4) :3-16

[4] A logarithmic-quadratic proximal method for variational inequalities [J].

Auslender, A ;

Teboulle, M ;

Ben-Tiba, S .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 1999, 12 (1-3) :31-40

[5] Lagrangian duality and related multiplier methods for variational inequality problems [J].

Auslender, A ;

Teboulle, M .

SIAM JOURNAL ON OPTIMIZATION, 2000, 10 (04) :1097-1115

[6]

Blum E., 1975, MAT OPTIMIERUNG ECON

[7] A generalized proximal point algorithm for the variational inequality problem in a Hilbert space [J].

Burachik, RS ;

Iusem, AN .

SIAM JOURNAL ON OPTIMIZATION, 1998, 8 (01) :197-216

[8] Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities [J].

Chen, X ;

Qi, L ;

Sun, D .

MATHEMATICS OF COMPUTATION, 1998, 67 (222) :519-540

[9] TRAFFIC EQUILIBRIUM AND VARIATIONAL-INEQUALITIES [J].

DAFERMOS, S .

TRANSPORTATION SCIENCE, 1980, 14 (01) :42-54

[10] NONLINEAR PROXIMAL POINT ALGORITHMS USING BREGMAN FUNCTIONS, WITH APPLICATIONS TO CONVEX-PROGRAMMING [J].

ECKSTEIN, J .

MATHEMATICS OF OPERATIONS RESEARCH, 1993, 18 (01) :202-226

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