Weak convergence theorem for a class of split variational inequality problems and applications in a Hilbert space

In this paper, we consider the algorithm proposed in recent years by Censor, Gibali and Reich, which solves split variational inequality problem, and Korpelevich’s extragradient method, which solves variational inequality problems. As our main result, we propose an iterative method for finding an el...

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Detalles Bibliográficos
Autores principales: Tian, Ming, Jiang, Bing-Nan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5445194/
https://www.ncbi.nlm.nih.gov/pubmed/28615916
http://dx.doi.org/10.1186/s13660-017-1397-9
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author Tian, Ming
Jiang, Bing-Nan
author_facet Tian, Ming
Jiang, Bing-Nan
author_sort Tian, Ming
collection PubMed
description In this paper, we consider the algorithm proposed in recent years by Censor, Gibali and Reich, which solves split variational inequality problem, and Korpelevich’s extragradient method, which solves variational inequality problems. As our main result, we propose an iterative method for finding an element to solve a class of split variational inequality problems under weaker conditions and get a weak convergence theorem. As applications, we obtain some new weak convergence theorems by using our weak convergence result to solve related problems in nonlinear analysis and optimization.
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spelling pubmed-54451942017-06-12 Weak convergence theorem for a class of split variational inequality problems and applications in a Hilbert space Tian, Ming Jiang, Bing-Nan J Inequal Appl Research In this paper, we consider the algorithm proposed in recent years by Censor, Gibali and Reich, which solves split variational inequality problem, and Korpelevich’s extragradient method, which solves variational inequality problems. As our main result, we propose an iterative method for finding an element to solve a class of split variational inequality problems under weaker conditions and get a weak convergence theorem. As applications, we obtain some new weak convergence theorems by using our weak convergence result to solve related problems in nonlinear analysis and optimization. Springer International Publishing 2017-05-25 2017 /pmc/articles/PMC5445194/ /pubmed/28615916 http://dx.doi.org/10.1186/s13660-017-1397-9 Text en © The Author(s) 2017 Open Access This 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 Research
Tian, Ming
Jiang, Bing-Nan
Weak convergence theorem for a class of split variational inequality problems and applications in a Hilbert space
title Weak convergence theorem for a class of split variational inequality problems and applications in a Hilbert space
title_full Weak convergence theorem for a class of split variational inequality problems and applications in a Hilbert space
title_fullStr Weak convergence theorem for a class of split variational inequality problems and applications in a Hilbert space
title_full_unstemmed Weak convergence theorem for a class of split variational inequality problems and applications in a Hilbert space
title_short Weak convergence theorem for a class of split variational inequality problems and applications in a Hilbert space
title_sort weak convergence theorem for a class of split variational inequality problems and applications in a hilbert space
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5445194/
https://www.ncbi.nlm.nih.gov/pubmed/28615916
http://dx.doi.org/10.1186/s13660-017-1397-9
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AT jiangbingnan weakconvergencetheoremforaclassofsplitvariationalinequalityproblemsandapplicationsinahilbertspace

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