General Iterative Methods for Semigroups of Nonexpansive Mappings Related to Optimization Problems

Abstract

In this article, we introduce two general iterative methods for a certain optimization problem of which the constrained set is the set of the solution set of the variational inequality problem for the fixed point set of nonexpansive semigroups in Hilbert spaces. Under some control conditions, we establish the strong convergence of the proposed methods to the fixed point set, which is the unique solution of a certain optimization problem. Applications to solutions of equilibrium problems are also presented.