Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space

被引：329

作者：

Censor, Yair ^{[1
]}

Gibali, Aviv ^{[2
]}

Reich, Simeon ^{[2
]}

机构：

[1] Univ Haifa, Dept Math, IL-31905 Haifa, Israel

[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

来源：

OPTIMIZATION METHODS & SOFTWARE | 2011年 / 26卷 / 4-5期

基金：

以色列科学基金会;

关键词：

extragradient method; Hilbert space; projection algorithm; subgradient; variational inequality; NONEXPANSIVE-MAPPINGS; PROJECTION ALGORITHMS; APPROXIMATIONS; OPTIMIZATION;

D O I：

10.1080/10556788.2010.551536

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We study two projection algorithms for solving the variational inequality problem in Hilbert space. One algorithm is a modified subgradient extragradient method in which an additional projection onto the intersection of two half-spaces is employed. Another algorithm is based on the shrinking projection method. We establish strong convergence theorems for both algorithms.

引用

页码：827 / 845

页数：19

共 27 条

[1] [Anonymous], 2003, SPRINGER SERIES OPER, DOI DOI 10.1007/978-0-387-21815-16
[2] A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space
Bauschke, Heinz H.
Combettes, Patrick L.
Luke, D. Russell
[J]. JOURNAL OF APPROXIMATION THEORY, 2006, 141 (01) : 63 - 69
[3] Construction of best Bregman approximations in reflexive Banach spaces
Bauschke, HH
Combettes, PL
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (12) : 3757 - 3766
[4] A weak-to-strong convergence principle for Fejer-monotone methods in Hilbert spaces
Bauschke, HH
Combettes, PL
[J]. MATHEMATICS OF OPERATIONS RESEARCH, 2001, 26 (02) : 248 - 264
[5] Projection algorithms for solving convex feasibility problems
Bauschke, HH
Borwein, JM
[J]. SIAM REVIEW, 1996, 38 (03) : 367 - 426
[6] An outer approximation method for the variational inequality problem
Burachik, RS
Lopes, JO
Svaiter, BF
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2005, 43 (06) : 2071 - 2088
[7] The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space
Censor, Y.
Gibali, A.
Reich, S.
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2011, 148 (02) : 318 - 335
[8] Censor Y., OPTIMIZATIO IN PRESS
[9] Computational acceleration of projection algorithms for the linear best approximation problem
Censor, Yair
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 416 (01) : 111 - 123
[10] Strong convergence of block-iterative outer approximation methods for convex optimization
Combettes, PL
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 38 (02) : 538 - 565

← 1 2 3 →