Le problème d'équilibre de Nash généralisé: définition, reformulation et méthodes de résolution

Abstract

The aim of this work is to study the generalized Nash equilibrium problem (for short, GNEP) and to reformulate it under different forms allowing to solve it numerically. First, we show that problem GNEP can be reduced to a variational inequality problem. Then, using the regularized Nikaido-Isoda-function, we present three reformulations of problem GNEP under the form of an optimization problem. Finally, we deduce a descent method with line search and a method with projections for solving it. For each of these methods, we give in detail the corresponding algorithms and we study their convergence. We test some of these algorithms on three problems to study their behavior.

Date of Award	28 Jun 2010
Original language	French
Supervisor	Jean-Jacques STRODIOT (Supervisor), Van Hien Nguyen (Jury), Joseph Winkin (Jury) & Philippe TOINT (Jury)