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

On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational... 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). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Optimization Theory and Applications Springer Journals

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

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Publisher
Springer US
Copyright
Copyright © 2018 by The Author(s)
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory
ISSN
0022-3239
eISSN
1573-2878
D.O.I.
10.1007/s10957-017-1214-0
Publisher site
See Article on Publisher Site

Abstract

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).

Journal

Journal of Optimization Theory and ApplicationsSpringer Journals

Published: Jan 18, 2018

References

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