Two projection algorithms for a class of split feasibility problems with jointly constrained Nash equilibrium models

ABSTRACT

In this paper, we consider a special split feasibility problem (SFP): $x\in C\text{and}Ax\in Q$ where C is the solution set of an equilibrium problem, Q is a convex subset in ${\mathcal{R}}^m$, and $A:{\mathcal{R}}^n\to {\mathcal{R}}^m$ 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 $Ax\in Q$. 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.

Keywords:

• Split feasibility
• equilibria
• projection method
• nash model

MSC:

• 47H05
• 47H07
• 47H10

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Open Fund of Tianjin Key Lab for Advanced Signal Processing [No. 2019ASP-TJ03] and Fundamental Research Funds for the Central Universities [No. 201919].