Algorithms And Applications Of The Generalized Nash Equilibria

In this diss(?)rtation, wo mainly investigate the algorithms and applications of the generalized Nash equilibrium problem. We design two methods for solving the generalized Nash equilibrium problem(GNEP). Also the applications of it are listed in this paper. Four main chapters are included as follows:Chapter 1 is the introduction. We describe the research situations of the generalized Nash equilibrium problem. The main contributions of this paper are also stated briefly.In Chapter 2,we present a new hybrid method for GNEP . At first, we reformulate generalized Nash equilibrium problem into an unconstrained optimization problem ,and then propose a new method for the unconstrained optimization problems and prove the global convergence.In Chapter 3, we design a projection algorithm for quasi-variational Inequalities and prove the global convergence of the algorithms.Due to generalized Nash equilibrium problem can be reformulated into a quasi-variational Inequality,so the method also can be applied to solve the generalized Nash equilibrium. Comparing with Noor's methods, the superiority of this method is that the application scope of it is more broader.Under a weaker condition the global convergence is guaranteed.And the iterative form is relatively simple.In Chapter 4,we mainly investigate the applications of the generalized Nash equilibrium problem. We introduce the specific applications of the generalized Nash equilibrium problem in abstract economy by Arrow and Dcbrcu,intcrnctswitching,environmental pollution control , the traffic internet switching and so on.