A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models

摘要

In this paper we propose an algorithm for solving the split feasibility problem xC,AxQ with C being the solution set of an equilibrium problem and A can be nonlinear. The proposed algorithm is a combination between the projection method for the equilibrium problem and the gradient method for the inclusion AxQ. The convergence of the algorithm is investigated. A numerical example for a jointly constrained Nash equilibrium model in electricity production market is provided to demonstrate the behavior of the algorithm.