Modified proximal-point algorithm for maximal monotone operators in banach spaces

被引：15

作者：

Li, L. ^{[1
,2
]}

Song, W. ^{[1
]}

机构：

[1] Harbin Normal Univ, Dept Math, Harbin 150080, Peoples R China

[2] NE Normal Univ, Dept Math, Changchun 130024, Peoples R China

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2008年 / 138卷 / 01期

关键词：

proximal-point algorithms; uniformly convex and smooth Banach spaces; maximal monotone operators; strong and weak convergence;

D O I：

10.1007/s10957-008-9370-x

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 introduce an iterative sequence for finding the solution to 0 is an element of T(v), where T : E paired right arrows E* is a maximal monotone operator in a smooth and uniformly convex Banach space E. This iterative procedure is a combination of iterative algorithms proposed by Kohsaka and Takahashi (Abstr. Appl. Anal. 3:239-249, 2004) and Kamamura, Kohsaka and Takahashi (Set-Valued Anal. 12:417-429, 2004). We prove a strong convergence theorem and a weak convergence theorem under different conditions respectively and give an estimate of the convergence rate of the algorithm. An application to minimization problems is given.

引用

页码：45 / 64

页数：20

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