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论文类型：期刊论文
发表时间：2014-10-01
发表刊物：JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
收录刊物：SCIE、Scopus
卷号：10
期号：4
页面范围：1091-1108
ISSN号：1547-5816
关键字：Nash equilibrium problem; generalized Nash equilibrium problem; logarithmic barrier function; quasi-variational inequalities; semismooth Newton method
摘要：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.