A splitting proximal point method for Nash-Cournot equilibrium models involving nonconvex cost functions

Le Dung Muu; Tran Dinh Quoc

arxiv: 1105.2632 · v1 · pith:LCPTVYK4new · submitted 2011-05-13 · 🧮 math.OC

A splitting proximal point method for Nash-Cournot equilibrium models involving nonconvex cost functions

Tran Dinh Quoc , Le Dung Muu This is my paper

classification 🧮 math.OC

keywords equilibriumpointlocalmethodnash-cournotnonconvexalgorithmconvergence

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Unlike convex case, a local equilibrium point of a nonconvex Nash-Cournot oligopolistic equilibrium problem may not be a global one. Finding such a local equilibrium point or even a stationary point of this problem is not an easy task. This paper deals with a numerical method for Nash-Cournot equilibrium models involving nonconvex cost functions. We develop a local method to compute a stationary point of this class of problems. The convergence of the algorithm is proved and its complexity is estimated under certain assumptions. Numerical examples are implemented to illustrate the convergence behavior of the proposed algorithm.

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