The subgradient extragradient method for solving pseudomonotone equilibrium and fixed point problems in Banach spaces. (9th December 2022)

• Record Type: Journal Article
• Authors: Jolaoso, L.O.
• Is Part Of: Optimization. Volume 71:Number 14(2022)
• Page Start: 4051
• Page End: 4081
• Publication Date: 2022-12-09
• Subjects: Equilibrium problem -- pseudomonotone -- self adaptive stepsize -- extragradient method -- Banach spaces; 65K15 -- 47J25 -- 65J15 -- 90C33; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1935935
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we introduce a self-adaptive subgradient extragradient method for finding a common element in the solution set of a pseudomonotone equilibrium problem and set of fixed points of a quasi- ϕ -nonexpansive mapping in 2-uniformly convex and uniformly smooth Banach spaces. The stepsize of the algorithm is selected self-adaptively which helps to prevent the necessity for prior estimates of the Lipschitz-like constants of the bifunction. A strong convergence result is proved under some mild conditions and some applications to Nash equilibrium problem and contact problem are presented to show the applicability of the result. Furthermore, some numerical examples are given to illustrate the efficiency and accuracy of the proposed method by comparing with other related methods in the literature.