A barrier function method for generalized Nash equilibrium problems
Jian Hou, Liwei Zhang · Journal of Industrial and Management Optimization · 2014
In this paper, we propose a barrier function method for the generalized Nashequilibrium problem (GNEP) which, in contrast to the standard Nashequilibrium problem (NEP), allows theconstraints for each player may depend on the rivals' strategies. We solve a sequence of NEPs, which are defined bylogarithmic barrier functions of the joint inequality constraints. We demonstrate, under suitable conditions, that any accumulation point of the solutions to the sequenceof NEPs isa solution to the GNEP. Moreover, asemismooth Newton method is used to solve the NEPs andsufficient conditions for the local superlinear convergence rate ofthe semismooth Newton method are derived. Finally, numerical resultsare reported to illustrate that the barrier approach for solvingthe GNEP is practical.