Extragradient Methods for Vector Equilibrium Problems in Banach Spaces. (4th July 2019)

• Record Type: Journal Article
• Authors: Iusem, Alfredo N.; Mohebbi, Vahid
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 9(2019)
• Page Start: 993
• Page End: 1022
• Publication Date: 2019-07-04
• Subjects: Equilibrium problem -- extragradient method -- Halpern regularization -- linesearch -- vector equilibrium problem -- vector valued bifunction; 90C25 -- 90C30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1578232
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We consider the vector equilibrium problem, which extends the scalar equilibrium problem to vector valued bifunctions, in a Banach space setting. We propose an extragradient method for solving this problem. Under suitable assumptions on the bifunction, we prove that the generated sequence is weakly convergent to a solution of the problem. Then, we propose a regularization procedure which ensures strong convergence of the generated sequence to a solution of the problem.