Some Algorithms For The Generalized Nash Equilibrium Problem

This thesis mainly investigates the algorithms of the generalized Nash equi-librium problem. Some methods are proposed to solve the generalized Nash equib-rium with different common strategy sets. The thesis consists of three chapters.Chapter 1 is the introduction of this thesis. We describe the research situ-ations of the generalized Nash equilibrium problem. The main contributions of this paper are also stated briefly.In Chapter 2, we present three methods for the generalized Nash equilibrium in which the common strategy set is compact and convex. At first, we reformulate the generalized Nash equilibrium into an unconstrained optimization problem. We can solve the generalized Nash equilibrium through solving this unconstrained optimization problem. Three algorithms are presented and the convergence are also proved under different assumption. The assumption used in the first method has existed in relevant literatures. Under the assumption, we can prove that the accumulation point of the algorithm is not only the stability of the generalized Nash equiribum, but also the normalized Nash equilibrium. Another assumption which is not stronger than that used in the first algorithm is given to prove the convergence of the other two methods, that is, the accumulation point of the algorithm is the normalized Nash equilibrium.In Chapter 3, we construct a new descent algorithm for the generalized Nash equilibrium problem with a compact and convex common strategy set via a new descent direction. Through modifying the descent direction of the relevant litera-tures, we obtain a new descent algorithm which has more applictions. The global convergence of the algorithm is also proved.