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
Descripción
Sumario: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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