The Ishikawa Subgradient Extragradient Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces. (3rd July 2020)

• Record Type: Journal Article
• Authors: Hy Duc, Manh; Nguyen Thi Thanh, Ha; Tran Thi Huyen, Thanh; Van Dinh, Bui
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 9(2020)
• Page Start: 1065
• Page End: 1088
• Publication Date: 2020-07-03
• Subjects: Pseudo-monotone -- equilibria -- Hilbert space -- Lipschitz-type continuous -- quasi-nonexpansive mapping -- strong convergence; 90C25 -- 90C33 -- 65K10 -- 65K15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1737937
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we introduce a novel algorithm for finding a common point of the solution set of a class of equilibrium problems involving pseudo-monotone bifunctions and satisfying the Lipschitz-type condition and the set of fixed points of a quasi-nonexpansive in a real Hilbert space. This algorithm can be considered as a combination of the subgradient extragradient method for equilibrium problems and the Ishikawa method for fixed point problems. The strong convergence of the iterates generated by the proposed method is obtained under the main assumptions that the fixed-point mapping is demiclosed at 0 and Lipschitz-type constant of the cost bifunction is unknown. Some numerical examples are implemented to show the computational efficiency of the proposed algorithm.