Two projection algorithms for a class of split feasibility problems with jointly constrained Nash equilibrium models. (3rd April 2021)

• Record Type: Journal Article
• Authors: Dong, Qiao-Li; Li, Xiao-Huan; Rassias, Themistocles M.
• Is Part Of: Optimization. Volume 70:Number 4(2021)
• Page Start: 871
• Page End: 897
• Publication Date: 2021-04-03
• Subjects: Split feasibility -- equilibria -- projection method -- nash model; 47H05 -- 47H07 -- 47H10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1753741
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we consider a special split feasibility problem (SFP): x ∈ C and A x ∈ Q where C is the solution set of an equilibrium problem, Q is a convex subset in R m, and A : R n → R m is a linear operator. We introduce two projection algorithms for solving the SFP by combining the projection method for the equilibrium problem and the gradient method for the inclusion A x ∈ Q . The proposed algorithms are shown to converge a solution of the SFP under weak conditions. We present a numerical example for a jointly constrained Nash equilibrium model in electricity production market to demonstrate the behaviour of the proposed algorithms.