Splitting Algorithms for Equilibrium Problems and Inclusion Problems on Hadamard Manifolds. (4th July 2021)

• Record Type: Journal Article
• Authors: Khammahawong, Konrawut; Kumam, Poom; Chaipunya, Parin
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 14(2021)
• Page Start: 1645
• Page End: 1682
• Publication Date: 2021-07-04
• Subjects: Equilibrium problems -- fixed points -- firmly nonexpansive mappings -- Hadamard manifolds -- inclusion problems -- monotone vector fields -- nonexpansive mappings; 26B25 -- 47H05 -- 47J25 -- 49J53 -- 58A05 -- 58B20 -- 58C30 -- 90C33; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1933523
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The aim of this article is to introduce new iterative algorithms for finding a common solution from the set of equilibrium points of an equilibrium problem and of singularities of an inclusion problem on Hadamard manifolds. We discuss some particular cases of the problem with the proposed algorithms. The convergence results of a sequence generated by the proposed algorithms are proved under mild assumptions on a Hadamard manifold. Moreover, we apply our results to solve optimization problems and variational inequality problems.