General Iterative Methods for Semigroups of Nonexpansive Mappings Related to Optimization Problems. (18th November 2019)

• Record Type: Journal Article
• Authors: Jeong, Jae Ug; Kim, Soo Hwan
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 15(2019)
• Page Start: 1768
• Page End: 1786
• Publication Date: 2019-11-18
• Subjects: General iterative method -- optimization problem -- nonexpansive semigroup -- common fixed point; 47H06 -- 47H09 -- 47J25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1636065
• Languages: English
• ISSNs: 0163-0563

Abstract

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.