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.
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页码：19 / 31
页数：13
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