Phan, V. (2018). On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities. Journal of Optimization Theory and Applications, 176(2), 399–409. https://doi.org/10.1007/s10957-017-1214-0
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Journal:
Journal of Optimization Theory and Applications
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ISSN:
0022-3239
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Date (published):
Feb-2018
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Number of Pages:
11
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Publisher:
SPRINGER/PLENUM PUBLISHERS
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Peer reviewed:
Yes
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Keywords:
Applied Mathematics; Control and Optimization; Management Science and Operations Research; Variational inequality; extragradient method; pseudo-monotonicity; weak convergence
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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 behaviour. The result obtained in this note extends some recent results in the literature; especially, it gives a positive answer to a question raised in Acta. Math. Vietnam, 41, 251-263 (2016).
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Research Areas:
Modelling and Simulation: 20% Mathematical and Algorithmic Foundations: 80%
