Strong convergence theorems for maximal monotone operators in Banach spaces

被引：2

作者：

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

Schaible, S. ^{[4
]}

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

机构：

[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan

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

[3] Sci Comp Key Lab Shanghai Univ, Shanghai 200234, Peoples R China

[4] Chung Yuan Christian Univ, Dept Appl Math, Chungli, Taiwan

来源：

OPTIMIZATION | 2010年 / 59卷 / 06期

基金：

美国国家科学基金会;

关键词：

maximal monotone operator; uniformly convex and uniformly smooth Banach space; generalized projection; technique of resolvent operators; iterative algorithms; strong convergence; GENERALIZED VARIATIONAL-INEQUALITIES; RELATIVELY NONEXPANSIVE-MAPPINGS; APPROXIMATE PROXIMAL ALGORITHMS; NONLINEAR OPERATORS; POINT ALGORITHM; HILBERT-SPACES; WEAK;

D O I：

10.1080/02331930902839426

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：

Let E be a uniformly convex and uniformly smooth Banach space with the dual E* and let T : E 2E* be a maximal monotone operator. By using the technique of resolvent operators and by using modified Ishikawa iteration and modified Halpern iteration for relatively non-expansive mappings, we suggest and analyse two iterative algorithms for finding an element x E such that 0 T(x). Strong convergence theorems for such iterative algorithms are proved. The ideas of these algorithms are applied to solve the problem of finding a minimizer of a convex function on E.

引用

页码：807 / 819

页数：13

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