Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces

Building upon the subgradient extragradient method proposed by Censor et al., we prove the strong convergence of the iterative sequence generated by a modification of this method by means of the Halpern method. We also consider the problem of finding a common element of the solution set of a variati...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2014-11, Vol.163 (2), p.399-412
Main Authors: Kraikaew, Rapeepan, Saejung, Satit
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Buildings
Calculus of Variations and Optimal Control
Optimization
Construction
Convergence
Engineering
Hilbert space
Inequalities
Inequality
Mapping
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Optimization techniques
Studies
Theory of Computation
Variance analysis
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Summary:Building upon the subgradient extragradient method proposed by Censor et al., we prove the strong convergence of the iterative sequence generated by a modification of this method by means of the Halpern method. We also consider the problem of finding a common element of the solution set of a variational inequality and the fixed-point set of a quasi-nonexpansive mapping with a demiclosedness property.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-013-0494-2