Finite Termination of Inexact Proximal Point Algorithms in Hilbert Spaces

被引：4

作者：

Wang, J. H. ^{[1
]}

Li, C. ^{[2
]}

Yao, J. -C. ^{[3
,4
]}

机构：

[1] Zhejiang Univ Technol, Dept Math, Hangzhou 310032, Zhejiang, Peoples R China

[2] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[3] Kaohsiung Med Univ, Ctr Fundamental Sci, Kaohsiung 80702, Taiwan

[4] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2015年 / 166卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Finite termination; Inexact proximal point algorithms; Maximal monotone; Projected gradient method; WEAK SHARP MINIMA; VARIATIONAL INEQUALITY PROBLEM; MAXIMAL MONOTONE-OPERATORS; ERROR-BOUNDS; CONVERGENCE ANALYSIS; CONVEX-OPTIMIZATION; BANACH-SPACES; FIXED-POINTS; INCLUSIONS; PROGRAMS;

D O I：

10.1007/s10957-014-0689-1

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：

In the present paper, we study the finite termination of sequences generated by inexact proximal point algorithms for finding zeroes of a maximal monotone (set-valued) operator on a Hilbert space. Under some mild conditions, we get that a sequence generated by inexact proximal point algorithm stops after a finite number of iterations. Our results extend the corresponding results in Rockafellar (SIAM J Control Optim 14:877-898, 1976). In particular, for optimization problems, our results improve corresponding results in Ferris (Math Progr 50:359-366, 1991). As applications, we obtain finite termination of projected gradient method.

引用

页码：188 / 212

页数：25

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