Extragradient subgradient methods for solving bilevel equilibrium problems

In this paper, we propose two algorithms for finding the solution of a bilevel equilibrium problem in a real Hilbert space. Under some sufficient assumptions on the bifunctions involving pseudomonotone and Lipschitz-type conditions, we obtain the strong convergence of the iterative sequence generate...

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Detalles Bibliográficos
Autores principales: Yuying, Tadchai, Dinh, Bui Van, Kim, Do Sang, Plubtieng, Somyot
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Review
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6267417/
https://www.ncbi.nlm.nih.gov/pubmed/30839868
http://dx.doi.org/10.1186/s13660-018-1898-1
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author Yuying, Tadchai
Dinh, Bui Van
Kim, Do Sang
Plubtieng, Somyot
author_facet Yuying, Tadchai
Dinh, Bui Van
Kim, Do Sang
Plubtieng, Somyot
author_sort Yuying, Tadchai
collection PubMed
description In this paper, we propose two algorithms for finding the solution of a bilevel equilibrium problem in a real Hilbert space. Under some sufficient assumptions on the bifunctions involving pseudomonotone and Lipschitz-type conditions, we obtain the strong convergence of the iterative sequence generated by the first algorithm. Furthermore, the strong convergence of the sequence generated by the second algorithm is obtained without a Lipschitz-type condition.
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spelling pubmed-62674172018-12-11 Extragradient subgradient methods for solving bilevel equilibrium problems Yuying, Tadchai Dinh, Bui Van Kim, Do Sang Plubtieng, Somyot J Inequal Appl Review In this paper, we propose two algorithms for finding the solution of a bilevel equilibrium problem in a real Hilbert space. Under some sufficient assumptions on the bifunctions involving pseudomonotone and Lipschitz-type conditions, we obtain the strong convergence of the iterative sequence generated by the first algorithm. Furthermore, the strong convergence of the sequence generated by the second algorithm is obtained without a Lipschitz-type condition. Springer International Publishing 2018-11-26 2018 /pmc/articles/PMC6267417/ /pubmed/30839868 http://dx.doi.org/10.1186/s13660-018-1898-1 Text en © The Author(s) 2018 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 Review
Yuying, Tadchai
Dinh, Bui Van
Kim, Do Sang
Plubtieng, Somyot
Extragradient subgradient methods for solving bilevel equilibrium problems
title Extragradient subgradient methods for solving bilevel equilibrium problems
title_full Extragradient subgradient methods for solving bilevel equilibrium problems
title_fullStr Extragradient subgradient methods for solving bilevel equilibrium problems
title_full_unstemmed Extragradient subgradient methods for solving bilevel equilibrium problems
title_short Extragradient subgradient methods for solving bilevel equilibrium problems
title_sort extragradient subgradient methods for solving bilevel equilibrium problems
topic Review
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6267417/
https://www.ncbi.nlm.nih.gov/pubmed/30839868
http://dx.doi.org/10.1186/s13660-018-1898-1
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AT kimdosang extragradientsubgradientmethodsforsolvingbilevelequilibriumproblems
AT plubtiengsomyot extragradientsubgradientmethodsforsolvingbilevelequilibriumproblems

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