Iterative Design for the Common Solution of Monotone Inclusions and Variational Inequalities

被引：1

作者：

Wei, Li ^{[1
]}

Shen, Xin-Wang ^{[1
]}

Agarwal, Ravi P. ^{[2
]}

机构：

[1] Hebei Univ Econ & Business, Sch Math & Stat, Shijiazhuang 050061, Hebei, Peoples R China

[2] Texas A&M Univ, Dept Math, Kingsville, TX 78363 USA

来源：

MATHEMATICS | 2021年 / 9卷 / 13期

关键词：

monotone inclusions; multi-choice iterative algorithm; theta-inversely strongly monotone operator; superposition perturbation; variational inequality; SPLITTING METHOD; CONVERGENCE; MAPPINGS; SETS;

D O I：

10.3390/math9131504

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Some new forward-backward multi-choice iterative algorithms with superposition perturbations are presented in a real Hilbert space for approximating common solution of monotone inclusions and variational inequalities. Some new ideas of constructing iterative elements can be found and strong convergence theorems are proved under mild restrictions, which extend and complement some already existing work.

引用

页数：21

共 26 条

[1]

Agarwal RP, 2009, TOPOL FIXED POINT TH, V6, P1, DOI 10.1007/978-0-387-75818-3_1

[2] PROPERTIES OF FIXED-POINT SETS OF NONEXPANSIVE MAPPINGS IN BANACH SPACES [J].

BRUCK, RE .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 179 (MAY) :251-262

[3] A New Double-Projection Method for Solving Variational Inequalities in Banach Spaces [J].

Cai, Gang ;

Gibali, Aviv ;

Iyiola, Olaniyi S. ;

Shehu, Yekini .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2018, 178 (01) :219-239

[4] A MODIFIED INERTIAL SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDOMONOTONE VARIATIONAL INEQUALITIES AND COMMON FIXED POINT PROBLEMS [J].

Ceng, L. C. ;

Petrusel, A. ;

Qin, X. ;

Yao, J. C. .

FIXED POINT THEORY, 2020, 21 (01) :93-108

[5] HYBRID VISCOSITY APPROXIMATION METHOD FOR ZEROS OF m-ACCRETIVE OPERATORS IN BANACH SPACES [J].

Ceng, Lu-Chuan ;

Ansari, Qamrul Hasan ;

Schaible, Siegfried ;

Yao, Jen-Chih .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2012, 33 (02) :142-165

[6] MANN-TYPE STEEPEST-DESCENT AND MODIFIED HYBRID STEEPEST-DESCENT METHODS FOR VARIATIONAL INEQUALITIES IN BANACH SPACES [J].

Ceng, Lu-Chuan ;

Ansari, Qamrul Hasan ;

Yao, Jen-Chih .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2008, 29 (9-10) :987-1033

[7]

Chen Q, 2019, J INTELLI MAT SYST S, P1

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

Combettes, PL ;

Wajs, VR .

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

[9] A strong convergence result involving an inertial forward-backward algorithm for monotone inclusions [J].

Dong, Qiaoli ;

Jiang, Dan ;

Cholamjiak, Prasit ;

Shehu, Yekini .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2017, 19 (04) :3097-3118

[10] A unified algorithm for solving variational inequality and fixed point problems with application to the split equality problem [J].

Jolaoso, L. O. ;

Taiwo, A. ;

Alakoya, T. O. ;

Mewomo, O. T. .

COMPUTATIONAL & APPLIED MATHEMATICS, 2020, 39 (01)

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