Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems
Yonghong Yao, Yeong‐Cheng Liou · Abstract and Applied Analysis · 2010
The purpose of this paper is to solve the minimization problem of finding x ∗ such that x ∗ = argmin 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 ∗ .