A SPLITTING PROXIMAL POINT METHOD FOR NASH-COURNOT EQUILIBRIUM MODELS INVOLVING NONCONVEX COST FUNCTIONS

摘要

Unlike convex case, a local equilibrium point of a nonconvex Nash-Cournot oligopolistic equilibrium problem may not be a global one. Finding such a point or even a stationary point of this problem is not an easy task. In this paper, we propose a numerical method for finding a stationary point of non-convex Nash-Cournot equilibrium problems. The convergence of the algorithm is proved and its complexity is estimated under certain assumptions. Numerical ex-amples are implemented to illustrate the convergence properties of the proposed algorithm.