A strong convergence theorem for a zero of the sum of a finite family of maximally monotone mappings

被引：2

作者：

Wega, Getahun B. ^{[1
]}

Zegeye, Habtu ^{[1
]}

Boikanyo, Oganeditse A. ^{[1
]}

机构：

[1] Botswana Int Univ Sci & Technol, Dept Math & Stat Sci, Pvt Bag 0016, Palapye, Botswana

来源：

DEMONSTRATIO MATHEMATICA | 2020年 / 53卷 / 01期

关键词：

firmly nonexpansive; Hilbert spaces; maximally monotone mapping; strong convergence; zero points; VISCOSITY APPROXIMATION METHODS; BACKWARD SPLITTING METHOD; PROXIMAL POINT ALGORITHM; ACCRETIVE-OPERATORS; SPACES; WEAK;

D O I：

10.1515/dema-2020-0010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this article is to study the method of approximation for zeros of the sum of a finite family of maximally monotone mappings and prove strong convergence of the proposed approximation method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems and provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

引用

页码：152 / 166

页数：15

共 35 条

[1] PROPERTIES OF ANGLE-BOUNDED AND N-CYCLICALLY MONOTONE OPERATORS [J].

BAILLON, JB ;

HADDAD, G .

ISRAEL JOURNAL OF MATHEMATICS, 1977, 26 (02) :137-150

[2] A weak-to-strong convergence principle for Fejer-monotone methods in Hilbert spaces [J].

Bauschke, HH ;

Combettes, PL .

MATHEMATICS OF OPERATIONS RESEARCH, 2001, 26 (02) :248-264

[3] Projection algorithms for solving convex feasibility problems [J].

Bauschke, HH ;

Borwein, JM .

SIAM REVIEW, 1996, 38 (03) :367-426

[4] Inducing strong convergence into the asymptotic behaviour of proximal splitting algorithms in Hilbert spaces [J].

Bot, Radu Ioan ;

Csetnek, Ernoe Robert ;

Meier, Dennis .

OPTIMIZATION METHODS & SOFTWARE, 2019, 34 (03) :489-514

[5] INFINITE PRODUCTS OF RESOLVENTS [J].

BREZIS, H ;

LIONS, PL .

ISRAEL JOURNAL OF MATHEMATICS, 1978, 29 (04) :329-345

[6] On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces [J].

Chang, SS .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 216 (01) :94-111

[7] Inertial forward-backward splitting method in Banach spaces with application to compressed sensing [J].

Cholamjiak, Prasit ;

Shehu, Yekini .

APPLICATIONS OF MATHEMATICS, 2019, 64 (04) :409-435

[8] An inertial forward-backward splitting method for solving inclusion problems in Hilbert spaces [J].

Cholamjiak, Watcharaporn ;

Cholamjiak, Prasit ;

Suantai, Suthep .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2018, 20 (01) :1-17

[9]

Combettes PL, 2009, J CONVEX ANAL, V16, P727

[10] Signal recovery by proximal forward-backward splitting [J].

Combettes, PL ;

Wajs, VR .

MULTISCALE MODELING & SIMULATION, 2005, 4 (04) :1168-1200

← 1 2 3 4 →