Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems
The purpose of this paper is to solve the minimization problem of finding x∗ such that x∗=argminx∈Γ‖x‖2, where Γ stands for the intersection set of the solution set of the equilibrium problem and the fixed points set of a nonexpansive mapping. We first present two new composite algorithms (one impli...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/763506 |
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| Summary: | The purpose of this paper is to solve the minimization problem of finding x∗ such that x∗=argminx∈Γ‖x‖2, where Γ stands for the intersection set of the solution set of the equilibrium problem and the fixed points set of a nonexpansive mapping. We first present two new composite algorithms (one implicit and one explicit). Further, we prove that the proposed composite algorithms converge strongly to x∗. |
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| ISSN: | 1085-3375 1687-0409 |