On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities

In infinite-dimensional Hilbert spaces, we prove that the iterative sequence generated by the extragradient method for solving pseudo-monotone variational inequalities converges weakly to a solution. A class of pseudo-monotone variational inequalities is considered to illustrate the convergent behav...

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Published inJournal of optimization theory and applications Vol. 176; no. 2; pp. 399 - 409
Main Author Vuong, Phan Tu
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2018
Springer Nature B.V
Subjects
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Control systems
Convergence
Cybernetics
Engineering
Estimates
Hilbert space
Inequalities
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Weak convergence
49M30
47J20
Variational inequality
49J40
Extragradient method
Pseudo-monotonicity
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Summary:In infinite-dimensional Hilbert spaces, we prove that the iterative sequence generated by the extragradient method for solving pseudo-monotone variational inequalities converges weakly to a solution. A class of pseudo-monotone variational inequalities is considered to illustrate the convergent behavior. The result obtained in this note extends some recent results in the literature; especially, it gives a positive answer to a question raised in Khanh (Acta Math Vietnam 41:251–263, 2016 ).
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-017-1214-0