Algorithms Of The Generalized Nash Equilibrium

In this dissertation,we mainly investigate the algorithms of the generalized Nash equilibrium problem(GNEP).We design three methods in solving the GNEP in this paper.The dissertation has four chapters.Chapter 1 is the introduction.We describe the research situations of the GNEP,the main results obtained in this thesis.In Chapter 2,we present a new method for the GNEP.At first,we reformulate the GNEP into an unconstrained optimization problem and propose a negative gradient algorithm for solving GNEP and prove the global convergence. At last,we give the preliminary numerical experiments which show that the algorithm has good behavior.In Chapter 3,we present a new method for the GNEP via a new descent direction.In Chapter 2,after obtained from the process of solving the negative gradient of the merit function,the variable y is taken to every plavers' payoff functions to calculate the corresponding partial derivative.On the basis of Chapter 2,using directly the variable y to construct a new descent direction,we present a new algorithm for solving the optimization problem which reformulated from GNEP in this paper.Under the condition that the solution set is nonempty,we show the global convergence of the algorithm.In addition,preliminary computational experience is also reported.In Chapter 4,we present a new type method for the GNEP.In this Chapter, combining the different descent directions which correspond to different parameters from above method,we obtain a new type descent algorithm.At last, numerical examples are given to show the effectiveness of this algorithm.