Modified extragradient algorithms for solving monotone variational inequalities and fixed point problems

In this paper, we investigate the monotone variational inequalities and fixed point problems in Hilbert spaces. Two modified extragradient algorithms are presented for finding a common element of the set of fixed points of a pseudocontractive operator and the set of solutions of the variational ineq...

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Bibliographic Details
Published inOptimization Vol. 69; no. 9; pp. 1987 - 2002
Main Authors Zhao, Xiaopeng, Yao, Yonghong
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 01.09.2020
Taylor & Francis LLC
Subjects
Algorithms
Extragradient algorithm
fixed point
Fixed points (mathematics)
Hilbert space
Inequalities
pseudocontraction
variational inequality
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Summary:In this paper, we investigate the monotone variational inequalities and fixed point problems in Hilbert spaces. Two modified extragradient algorithms are presented for finding a common element of the set of fixed points of a pseudocontractive operator and the set of solutions of the variational inequality problem. Weak and strong convergence of the suggested algorithms are proved.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2019.1711087