A STRONG CONVERGENCE THEOREM FOR A PROXIMAL-TYPE ALGORITHM IN REFLEXIVE BANACH SPACES

被引：2

作者：

Reich, Simeon ^{[1
]}

Sabach, Shoham ^{[1
]}

机构：

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2009年 / 10卷 / 03期

基金：

以色列科学基金会;

关键词：

Banach space; Bregman projection; Legendre function; maximal monotone operator; monotone operator; proximal point algorithm; resolvent; totally convex function; TOTAL CONVEXITY; MONOTONE-OPERATORS; POINT; PROJECTION; WEAK;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish a strong convergence theorem for a proximal-type algorithm which approximates (common) zeroes of maximal monotone operators in reflexive Banach spaces This algorithm employs a well-chosen convex function The behavior of the algorithm in the presence of computational errors and in the case of zero free operators is also analyzed. Finally, we mention several corollaries, variations and applications

引用

页码：471 / 485

页数：15

共 39 条

[21] NONLINEAR PROXIMAL POINT ALGORITHMS USING BREGMAN FUNCTIONS, WITH APPLICATIONS TO CONVEX-PROGRAMMING
ECKSTEIN, J
[J]. MATHEMATICS OF OPERATIONS RESEARCH, 1993, 18 (01) : 202 - 226
[22] GULER O, 1991, SIAM J CONTROL OPTIM, V29, P403, DOI 10.1137/0329022
[23] Weak and strong convergence of solutions to accretive operator inclusions and applications
Kamimura, S
Takahashi, W
[J]. SET-VALUED ANALYSIS, 2000, 8 (04): : 361 - 374
[24] Approximating solutions of maximal monotone operators in Hilbert spaces
Kamimura, S
Takahashi, W
[J]. JOURNAL OF APPROXIMATION THEORY, 2000, 106 (02) : 226 - 240
[25] Kamimura SJ, 2003, SIAM J OPTIMIZ, V13, P938
[26] MARTINET R, 1970, RIRO, V4, P154
[27] STRONG CONVERGENCE OF CONTRACTION SEMIGROUPS AND OF ITERATIVE METHODS FOR ACCRETIVE OPERATORS IN BANACH-SPACES
NEVANLINNA, O
REICH, S
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1979, 32 (01) : 44 - 58
[28] A strongly convergent hybrid proximal method in Banach spaces
Otero, RG
Svaiter, BF
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 289 (02) : 700 - 711
[29] PASCAH D, 1978, NONLINEAR MAPPINGS M
[30] WEAK CONVERGENCE THEOREMS FOR NONEXPANSIVE MAPPINGS IN BANACH-SPACES
REICH, S
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1979, 67 (02) : 274 - 276

← 1 2 3 4 →