Parallel Algorithms for Solving a Class of Variational Inequalities over the Common Fixed Points Set of a Finite Family of Demicontractive Mappings. (26th October 2018)

• Record Type: Journal Article
• Authors: Anh, Tran Viet; Muu, Le Dung; Son, Dang Xuan
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 14(2018)
• Page Start: 1477
• Page End: 1494
• Publication Date: 2018-10-26
• Subjects: Common fixed point -- demicontractive mapping -- equilibrium constraint -- parallel method -- variational inequality; 49J40 -- 90C33 -- 47H17; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1485695
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We propose parallel algorithms for solving a class of variational inequalities over the set of common fixed points for a finite family of demicontractive mappings in real Hilbert spaces. Under some suitable conditions, we prove that the sequence generated by the proposed algorithms converges strongly to a solution of the problem. We apply the proposed algorithms to strongly monotone variational inequality problems with pseudomonotone equilibrium constraints by defining a quasi-nonexpansive and demi-closed mapping whose fixed point set coincides with the solution set of the equilibrium problem.