# American Institute of Mathematical Sciences

October  2014, 10(4): 1091-1108. doi: 10.3934/jimo.2014.10.1091

## A barrier function method for generalized Nash equilibrium problems

 1 Institute of ORCT, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China 2 Institute of ORCT, School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024

Received  January 2013 Revised  December 2013 Published  February 2014

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.
Citation: Jian Hou, Liwei Zhang. A barrier function method for generalized Nash equilibrium problems. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1091-1108. doi: 10.3934/jimo.2014.10.1091
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