BB Step With Adaptive Projection Method For Solving The Generalized Nash Equilibrium Problem

The generalized Nash equilibrium problem (GNEP) is a core concept of the noncooperative game in which the strategy set of each player, as well as his payoff function, depends on the rival players’ strategies. It is widely used in economics, management sciences and transports Research, but how to solve the generalized Nash equilibrium problem effectively is still a subject of great concerns. The meth-ods to solve the generalized Nash equilibrium problem are roughly divided into two kinds:one is using of Gap function, Nikaido-Isoda function, penalty function and pa-rameterized VI to transform GNEP into the corresponding optimization problem or a variational inequality(VI). The other is reformulating GNEP as a quasi-variational inequality (QVI) and then using projection methods and Newton’s method to solve the reformulated problems.In this paper, we present a self-adaptive projection method with the BB stepsize for solving generalized Nash equilibrium problems. First, we rewrite the generalized Nash equilibrium problem (GNEP) as a a quasi-variational inequality (QVI); Then, we combine the BB stepsize and the nonmonotonic idea to the quasi-variational inequality (QVI). At the same time, we prove the global convergence of the new al-gorithm under some resonable conditions. Some computational results are reported, which illustrate the new method is efficient.