An Improved Projection Method For Generalized Nash Equilibrium Problems

Nash equilibrium problem is a vital definition of economics.The generalized Nash equilibrium problem is an expanded definition of Nash equilibrium problem,whose strategy set of each player depends on the other rivals' decisions.It ha.s large meaning of applicability and practicability.Nowadays,the research for solving this problem is still in its infancy.Recently,it has been studied by lots of researcher-s.If every player's objective function and constraint set are con-vex,Nash equilibrium problem is equivalent to variational inequali-ties problem and generalized Nash equilibrium problem is equivalent to quasi variational inequalities problem.As a result,the algorithms which solve quasi-variational inequalities problem can be used to solve generalized Nash equilibrium problem.There are many algorithms to solve quasi-variational inequalities problems,such as Newton-type methods,proximal point methods,splitting methods and projection-type methods.Projection-type methods can be used to solve the corresponding monotone quasi-variational inequalities problem.In this paper,we proposed an accelerated method based on the half-space projection algorithm.At each iteration,we obtain a prediction point first by the half-space projection method.Then we use the extrapolation tech-nique to obtain the next iterate point.We prove that the sequence generated from the algorithm is convergent.Numerical results show that our algorithm is effective.