Algorithmic Approach to a Minimization Problem

Algorithmic Approach to a Minimization Problem

We first construct an implicit algorithm for solving the minimization problem minx∈Ω∥x∥ , where Ω is the intersection set of the solution set of some equilibrium problem, the fixed points set of a nonexpansive mapping, and the solution set of some variational inequality. Further, we suggest an expli...

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Main Authors: Yonghong Yao, Shin Min Kang, Yeong-Cheng Liou, Zhitao Wu
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/310801
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spelling doaj-39e7edf6f9e54c08a79dbc9634ec3e642020-11-24T22:00:24ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/310801310801Algorithmic Approach to a Minimization ProblemYonghong Yao0Shin Min Kang1Yeong-Cheng Liou2Zhitao Wu3Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaDepartment of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of KoreaDepartment of Information Management, Cheng Shiu University, Kaohsiung 833, TaiwanDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaWe first construct an implicit algorithm for solving the minimization problem minx∈Ω∥x∥ , where Ω is the intersection set of the solution set of some equilibrium problem, the fixed points set of a nonexpansive mapping, and the solution set of some variational inequality. Further, we suggest an explicit algorithm by discretizing this implicit algorithm. We prove that the proposed implicit and explicit algorithms converge strongly to a solution of the above minimization problem.http://dx.doi.org/10.1155/2012/310801
collection DOAJ
language English
format Article
sources DOAJ
author Yonghong Yao
Shin Min Kang
Yeong-Cheng Liou
Zhitao Wu
spellingShingle Yonghong Yao
Shin Min Kang
Yeong-Cheng Liou
Zhitao Wu
Algorithmic Approach to a Minimization Problem
Abstract and Applied Analysis
author_facet Yonghong Yao
Shin Min Kang
Yeong-Cheng Liou
Zhitao Wu
author_sort Yonghong Yao
title Algorithmic Approach to a Minimization Problem
title_short Algorithmic Approach to a Minimization Problem
title_full Algorithmic Approach to a Minimization Problem
title_fullStr Algorithmic Approach to a Minimization Problem
title_full_unstemmed Algorithmic Approach to a Minimization Problem
title_sort algorithmic approach to a minimization problem
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description We first construct an implicit algorithm for solving the minimization problem minx∈Ω∥x∥ , where Ω is the intersection set of the solution set of some equilibrium problem, the fixed points set of a nonexpansive mapping, and the solution set of some variational inequality. Further, we suggest an explicit algorithm by discretizing this implicit algorithm. We prove that the proposed implicit and explicit algorithms converge strongly to a solution of the above minimization problem.
url http://dx.doi.org/10.1155/2012/310801
work_keys_str_mv AT yonghongyao algorithmicapproachtoaminimizationproblem
AT shinminkang algorithmicapproachtoaminimizationproblem
AT yeongchengliou algorithmicapproachtoaminimizationproblem
AT zhitaowu algorithmicapproachtoaminimizationproblem
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