Inertial-Like Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive and Strictly Pseudocontractive Mappings

被引：12

作者：

Ceng, Lu-Chuan ^{[1
]}

Petrusel, Adrian ^{[2
]}

Wen, Ching-Feng ^{[3
,4
,5
]}

Yao, Jen-Chih ^{[6
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Babes Bolyai Univ, Dept Math, Cluj Napoca 400084, Romania

[3] Kaohsiung Med Univ, Ctr Fundamental Sci, Kaohsiung 80708, Taiwan

[4] Kaohsiung Med Univ, Res Ctr Nonliear Anal & Optimizat, Kaohsiung 80708, Taiwan

[5] Kaohsiung Med Univ Hosp, Dept Med Res, Kaohsiung 80708, Taiwan

[6] China Med Univ Hosp, Res Ctr Interneural Comp, Taichung 40402, Taiwan

来源：

MATHEMATICS | 2019年 / 7卷 / 09期

关键词：

inertial-like subgradient-like extragradient method with line-search process; pseudomonotone variational inequality problem; asymptotically nonexpansive mapping; strictly pseudocontractive mapping; sequentially weak continuity; STRONG-CONVERGENCE; ACCRETIVE-OPERATORS; NONLINEAR MAPPINGS; SPLIT FEASIBILITY; FINITE FAMILY; ZERO POINTS; SYSTEMS;

D O I：

10.3390/math7090860

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let VIP indicate the variational inequality problem with Lipschitzian and pseudomonotone operator and let CFPP denote the common fixed-point problem of an asymptotically nonexpansive mapping and a strictly pseudocontractive mapping in a real Hilbert space. Our object in this article is to establish strong convergence results for solving the VIP and CFPP by utilizing an inertial-like gradient-like extragradient method with line-search process. Via suitable assumptions, it is shown that the sequences generated by such a method converge strongly to a common solution of the VIP and CFPP, which also solves a hierarchical variational inequality (HVI).

引用

页数：19

共 40 条

[1] Regularization of proximal point algorithms in Hadamard manifolds [J].

Ansari, Qamrul Hasan ;

Babu, Feeroz ;

Yao, Jen-Chih .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2019, 21 (01)

[2]

Bin Dehaish BA, 2015, J NONLINEAR CONVEX A, V16, P1321

[3] A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces [J].

Bin Dehaish, Buthinah A. ;

Latif, Abdul ;

Bakodah, Huda O. ;

Qin, Xiaolong .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015,

[4] Strong convergence results for variational inequalities and fixed point problems using modified viscosity implicit rules [J].

Cai, Gang ;

Shehu, Yekini ;

Iyiola, Olaniyi Samuel .

NUMERICAL ALGORITHMS, 2018, 77 (02) :535-558

[5]

Ceng LC, 2014, J NONLINEAR CONVEX A, V15, P219

[6] Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem [J].

Ceng, L. -C. ;

Ansari, Q. H. ;

Yao, J. -C. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (04) :2116-2125

[7] Some iterative methods for finding fixed points and for solving constrained convex minimization problems [J].

Ceng, L. -C. ;

Ansari, Q. H. ;

Yao, J. -C. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (16) :5286-5302

[8] An extragradient method for solving split feasibility and fixed point problems [J].

Ceng, L-C ;

Ansari, Q. H. ;

Yao, J-C .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 64 (04) :633-642

[9]

CENG LC, 2019, MATHEMATICS-BASEL, V7, DOI DOI 10.3390/math7040338

[10]

CENG LC, 2019, OPTIMIZATION 0727, DOI DOI 10.1080/02331934.2019.1647203

← 1 2 3 4 →