Convergence of the Modified Extragradient Method for Variational Inequalities with Non-Lipschitz Operators

We propose a modified extragradient method with dynamic step size adjustment to solve variational inequalities with monotone operators acting in a Hilbert space. In addition, we consider a version of the method that finds a solution of a variational inequality that is also a fixed point of a quasi-n...

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Published inCybernetics and systems analysis Vol. 51; no. 5; pp. 757 - 765
Main Authors Denisov, S. V., Semenov, V. V., Chabak, L. M.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2015
Springer
Springer Nature B.V
Subjects
Adjustment
Algorithms
Analysis
Artificial Intelligence
Computer science
Continuity
Control
Convergence
Cybernetics
Dynamics
Game theory
Hilbert space
Inequalities
Management science
Mathematics
Mathematics and Statistics
Methods
Operators
Processor Architectures
Software Engineering/Programming and Operating Systems
Studies
Systems analysis
Systems Theory
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Summary:We propose a modified extragradient method with dynamic step size adjustment to solve variational inequalities with monotone operators acting in a Hilbert space. In addition, we consider a version of the method that finds a solution of a variational inequality that is also a fixed point of a quasi-nonexpansive operator. We establish the weak convergence of the methods without any Lipschitzian continuity assumption on operators.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-015-9768-z