Convergence of Tseng-type self-adaptive algorithms for variational inequalities and fixed point problems

被引：68

作者：

Yao, Yonghong ^{[1
,2
]}

Shahzad, Naseer ^{[3
]}

Yao, Jen-Chih ^{[4
]}

机构：

[1] Tiangong Univ, Sch Math Sci, Tianjin 300387, Peoples R China

[2] North Minzu Univ, Key Lab Intelligent Informat & Big Data Proc Ning, Yinchuan 750021, Ningxia, Peoples R China

[3] King Abdulaziz Univ, Dept Math, POB 80203, Jeddah 21589, Saudi Arabia

[4] China Med Univ, Ctr Gen Educ, Taichung 40402, Taiwan

来源：

CARPATHIAN JOURNAL OF MATHEMATICS | 2021年 / 37卷 / 03期

关键词：

Variational inequality; fixed point; pseudomonotone operators; pseudocontractive operators; Tseng-type algorithm; EXTRAGRADIENT METHOD; COMPLEMENTARITY-PROBLEMS; WEAK-CONVERGENCE; GRADIENT METHODS; PROJECTION;

D O I：

10.37193/CJM.2021.03.15

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a Tseng-type self-adaptive algorithm for solving a variational inequality and a fixed point problem involving pseudomonotone and pseudocontractive operators in Hilbert spaces. A weak convergent result for such algorithm is proved under a weaker assumption than sequentially weakly continuous imposed on the pseudomonotone operator. Some corollaries are also included.

引用

页码：541 / 550

页数：10

共 28 条

[1] Newton-Like Dynamics and Forward-Backward Methods for Structured Monotone Inclusions in Hilbert Spaces [J].

Abbas, B. ;

Attouch, H. ;

Svaiter, Benar F. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2014, 161 (02) :331-360

[2]

Bauschke HH, 2011, CMS BOOKS MATH, P1, DOI 10.1007/978-1-4419-9467-7

[3] The forward-backward-forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces [J].

Bot, R., I ;

Csetnek, E. R. ;

Vuong, P. T. .

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2020, 287 (01) :49-60

[4] On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators [J].

Cai, Xingju ;

Gu, Guoyong ;

He, Bingsheng .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2014, 57 (02) :339-363

[5] 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

[6] Weak Convergence of an Iterative Method for Pseudomonotone Variational Inequalities and Fixed-Point Problems [J].

Ceng, L. C. ;

Teboulle, M. ;

Yao, J. C. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2010, 146 (01) :19-31

[7] Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space [J].

Censor, Yair ;

Gibali, Aviv ;

Reich, Simeon .

OPTIMIZATION, 2012, 61 (09) :1119-1132

[8] PSEUDOMONOTONE COMPLEMENTARITY-PROBLEMS IN HILBERT-SPACE [J].

COTTLE, RW ;

YAO, JC .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1992, 75 (02) :281-295

[9] Modified extragradient-like algorithms with new stepsizes for variational inequalities [J].

Dang Van Hieu ;

Pham Ky Anh ;

Le Dung Muu .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2019, 73 (03) :913-932

[10] The extragradient algorithm with inertial effects for solving the variational inequality [J].

Dong, Qiao-Li ;

Lu, Yan-Yan ;

Yang, Jinfeng .

OPTIMIZATION, 2016, 65 (12) :2217-2226

← 1 2 3 →