A BARRIER FUNCTION METHOD FOR GENERALIZED NASH EQUILIBRIUM PROBLEMS

Indexed by:期刊论文

Journal:JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

Included Journals:SCIE、Scopus

Volume:10

Issue:4

Page Number:1091-1108

ISSN No.:1547-5816

Key Words:Nash equilibrium problem; generalized Nash equilibrium problem; logarithmic barrier function; quasi-variational inequalities; semismooth Newton method

Abstract:In this paper, we propose a barrier function method for the generalized Nash equilibrium problem (GNEP) which, in contrast to the standard Nash equilibrium problem (NEP), allows the constraints for each player may depend on the rivals' strategies. We solve a sequence of NEPs, which are defined by logarithmic barrier functions of the joint inequality constraints. We demonstrate, under suitable conditions, that any accumulation point of the solutions to the sequence of NEPs is a solution to the GNEP. Moreover, a semismooth Newton method is used to solve the NEPs and sufficient conditions for the local superlinear convergence rate of the semismooth Newton method are derived. Finally, numerical results are reported to illustrate that the barrier approach for solving the GNEP is practical.

Date of Publication:2014-10-01