Two projection algorithms for a class of split feasibility problems with jointly constrained Nash equilibrium models
Qiao‐Li Dong, Xiaohuan Li, Themistocles M. Rassias · Optimization · 2020
In this paper, we consider a special split feasibility problem (SFP): x∈CandAx∈Q where C is the solution set of an equilibrium problem, Q is a convex subset in Rm, and A:Rn→Rm 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 Ax∈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.