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: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/310801 |
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| _version_ | 1832558788799889408 |
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| author | Yonghong Yao Shin Min Kang Yeong-Cheng Liou Zhitao Wu |
| author_facet | Yonghong Yao Shin Min Kang Yeong-Cheng Liou Zhitao Wu |
| author_sort | Yonghong Yao |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-39e7edf6f9e54c08a79dbc9634ec3e64 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-39e7edf6f9e54c08a79dbc9634ec3e642025-02-03T01:31:34ZengWileyAbstract 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 |
| spellingShingle | Yonghong Yao Shin Min Kang Yeong-Cheng Liou Zhitao Wu Algorithmic Approach to a Minimization Problem Abstract and Applied Analysis |
| title | 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_short | Algorithmic Approach to a Minimization Problem |
| title_sort | algorithmic approach to a 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 |