Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems
We introduce and analyze a new hybrid extragradient-like viscosity iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinit...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/120172 |
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| _version_ | 1832550077211607040 |
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| author | Lu-Chuan Ceng Chi-Ming Chen Chin-Tzong Pang |
| author_facet | Lu-Chuan Ceng Chi-Ming Chen Chin-Tzong Pang |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | We introduce and analyze a new hybrid extragradient-like viscosity iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some mild conditions, we prove the strong convergence of the sequence generated by the proposed algorithm to a common solution of these three problems which also solves an optimization problem. |
| format | Article |
| id | doaj-art-6fd5876bd88a43f78b3c7c327e0a46b5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6fd5876bd88a43f78b3c7c327e0a46b52025-02-03T06:07:47ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/120172120172Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization ProblemsLu-Chuan Ceng0Chi-Ming Chen1Chin-Tzong Pang2Department of Mathematics, Shanghai Normal University, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, ChinaDepartment of Applied Mathematics, National Hsinchu University of Education, Hsinchu 30033, TaiwanDepartment of Information Management, Yuan Ze University, Chung-Li 32003, TaiwanWe introduce and analyze a new hybrid extragradient-like viscosity iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some mild conditions, we prove the strong convergence of the sequence generated by the proposed algorithm to a common solution of these three problems which also solves an optimization problem.http://dx.doi.org/10.1155/2014/120172 |
| spellingShingle | Lu-Chuan Ceng Chi-Ming Chen Chin-Tzong Pang Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems Abstract and Applied Analysis |
| title | Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems |
| title_full | Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems |
| title_fullStr | Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems |
| title_full_unstemmed | Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems |
| title_short | Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems |
| title_sort | hybrid extragradient like viscosity methods for generalized mixed equilibrium problems variational inclusions and optimization problems |
| url | http://dx.doi.org/10.1155/2014/120172 |
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