Weak Convergence of an Iterative Method for Pseudomonotone Variational Inequalities and Fixed-Point Problems

被引：92

作者：

Ceng, L. C. ^{[2
,3
]}

Teboulle, M. ^{[4
]}

Yao, J. C. ^{[1
]}

机构：

[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[3] Sci Comp Key Lab Shanghai Univ, Shanghai, Peoples R China

[4] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2010年 / 146卷 / 01期

基金：

美国国家科学基金会;

关键词：

Variational inequalities; Nonexpansive mappings; Extragradient methods; Approximate proximal methods; Pseudomonotone mappings; Fixed points; Weak convergence; Opial condition; NONEXPANSIVE-MAPPINGS; EXTRAGRADIENT METHOD; MONOTONE; THEOREM;

D O I：

10.1007/s10957-010-9650-0

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：

We consider an iterative scheme for finding a common element of the set of solutions of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of N nonexpansive mappings. The proposed iterative method combines two well-known schemes: extragradient and approximate proximal methods. We derive a necessary and sufficient condition for weak convergence of the sequences generated by the proposed scheme.

引用

页码：19 / 31

页数：13

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