Two projection algorithms for a class of split feasibility problems with jointly constrained Nash equilibrium models. (3rd April 2021) - Dong, Qiao-Li; Li, Xiao-Huan; Rassias, Themistocles M.
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.