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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 inequalities
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 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).
0022-3239
399-409
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf

Vuong, Phan Tu (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. (doi:10.1007/s10957-017-1214-0).

Record type: Article

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).

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Accepted/In Press date: 1 January 2017
e-pub ahead of print date: 18 January 2018
Published date: 1 February 2018

Identifiers

Local EPrints ID: 434647
URI: http://eprints.soton.ac.uk/id/eprint/434647
DOI: doi:10.1007/s10957-017-1214-0
ISSN: 0022-3239
PURE UUID: f66be5ca-3765-4897-82e8-459411243877
ORCID for Phan Tu Vuong: ORCID iD orcid.org/0000-0002-1474-994X

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Date deposited: 04 Oct 2019 16:30
Last modified: 16 Mar 2024 04:42

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Author: Phan Tu Vuong ORCID iD

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