WEAK CONVERGENCE THEOREM BY A MODIFIED EXTRAGRADIENT METHOD FOR VARIATIONAL INCLUSIONS,VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS

被引：0

作者：

Ceng, Lu-Chuan ^{[1
,2
]}

Guu, Sy-Ming ^{[3
]}

Yao, Jen-Chih ^{[4
,5
]}

机构：

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

[2] Sci Comp Key Lab Shanghai Univ, Shanghai 200041, Peoples R China

[3] Chang Gung Univ, Sch Business, Coll Management, Tao Yuan 333, Taiwan

[4] Kaohsiung Med Univ, Ctr Gen Educ, Kaohsiung 807, Taiwan

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

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2013年 / 14卷 / 01期

基金：

美国国家科学基金会;

关键词：

Variational inclusion; variational inequality; nonexpansive mapping; inverse strongly monotone mapping; maximal monotone mapping; weak convergence; NONEXPANSIVE-MAPPINGS; INCLUSIONS; OPERATORS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the problem of finding common solutions of variational inclusions, variational inequalities and fixed point problems in real Hilbert spaces. Motivated by Nadezhkina and Takahashi's extragradient method [N. Nadezhkina, W. Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 128 (2006) 191-201], we propose and analyze a modified extragradient algorithm for finding common solutions. It is proven that three sequences generated by this algorithm converge weakly to the same common solution under very mild conditions by virtue of the Opial condition of Hilbert spaces, the demi-closedness principle for nonexpansive mappings and the coincidence of solutions of variational inequalities with zeros of maximal monotone operators.

引用

页码：21 / 31

页数：11

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