Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems

Yonghong Yao and Yeong-Cheng Liou

Abstract and Applied Analysis, 2010, vol. 2010, 1-19

Abstract:

The purpose of this paper is to solve the minimization problem of finding x ∗ such that x ∗ = arg min x ∈ 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 ∗ .

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:763506

DOI: 10.1155/2010/763506

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