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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Detalles Bibliográficos
Autor principal: Vuong, Phan Tu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6951821/
https://www.ncbi.nlm.nih.gov/pubmed/31983774
http://dx.doi.org/10.1007/s10957-017-1214-0
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author Vuong, Phan Tu
author_facet Vuong, Phan Tu
author_sort Vuong, Phan Tu
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description 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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spelling pubmed-69518212020-01-23 On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities Vuong, Phan Tu J Optim Theory Appl Article 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). Springer US 2018-01-18 2018 /pmc/articles/PMC6951821/ /pubmed/31983774 http://dx.doi.org/10.1007/s10957-017-1214-0 Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Vuong, Phan Tu
On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities
title On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities
title_full On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities
title_fullStr On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities
title_full_unstemmed On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities
title_short On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities
title_sort on the weak convergence of the extragradient method for solving pseudo-monotone variational inequalities
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6951821/
https://www.ncbi.nlm.nih.gov/pubmed/31983774
http://dx.doi.org/10.1007/s10957-017-1214-0
work_keys_str_mv AT vuongphantu ontheweakconvergenceoftheextragradientmethodforsolvingpseudomonotonevariationalinequalities

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