Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems
It is well known that the gradient-projection algorithm (GPA) for solving constrained convex minimization problems has been proven to have only weak convergence unless the underlying Hilbert space is finite dimensional. In this paper, we introduce a new hybrid gradient-projection algorithm for solvi...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/678353 |
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| _version_ | 1832561459202097152 |
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| author | Lu-Chuan Ceng Ching-Feng Wen |
| author_facet | Lu-Chuan Ceng Ching-Feng Wen |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | It is well known that the gradient-projection algorithm (GPA) for solving constrained convex minimization problems has been proven to have only weak convergence unless the underlying Hilbert space is finite dimensional. In this paper, we introduce a new hybrid gradient-projection algorithm for solving constrained convex minimization problems with generalized mixed equilibrium problems in a real Hilbert space. It is proven that three sequences generated by this algorithm converge strongly to the unique solution of some variational inequality, which is also a common element of the set of solutions of a constrained convex minimization problem, the set of solutions of a generalized mixed equilibrium problem, and the set of fixed points of a strict pseudocontraction in a real Hilbert space. |
| format | Article |
| id | doaj-art-cad78a4c4c104387a03aa8bc7246ac00 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-cad78a4c4c104387a03aa8bc7246ac002025-02-03T01:25:07ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/678353678353Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium ProblemsLu-Chuan Ceng0Ching-Feng Wen1Department of Mathematics, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai Normal University, Shanghai 200234, ChinaCenter for General Education, Kaohsiung Medical University, Kaohsiung 80708, TaiwanIt is well known that the gradient-projection algorithm (GPA) for solving constrained convex minimization problems has been proven to have only weak convergence unless the underlying Hilbert space is finite dimensional. In this paper, we introduce a new hybrid gradient-projection algorithm for solving constrained convex minimization problems with generalized mixed equilibrium problems in a real Hilbert space. It is proven that three sequences generated by this algorithm converge strongly to the unique solution of some variational inequality, which is also a common element of the set of solutions of a constrained convex minimization problem, the set of solutions of a generalized mixed equilibrium problem, and the set of fixed points of a strict pseudocontraction in a real Hilbert space.http://dx.doi.org/10.1155/2012/678353 |
| spellingShingle | Lu-Chuan Ceng Ching-Feng Wen Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems Journal of Function Spaces and Applications |
| title | Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems |
| title_full | Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems |
| title_fullStr | Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems |
| title_full_unstemmed | Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems |
| title_short | Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems |
| title_sort | hybrid gradient projection algorithm for solving constrained convex minimization problems with generalized mixed equilibrium problems |
| url | http://dx.doi.org/10.1155/2012/678353 |
| work_keys_str_mv | AT luchuanceng hybridgradientprojectionalgorithmforsolvingconstrainedconvexminimizationproblemswithgeneralizedmixedequilibriumproblems AT chingfengwen hybridgradientprojectionalgorithmforsolvingconstrainedconvexminimizationproblemswithgeneralizedmixedequilibriumproblems |