Le principe du problème auxiliaire pour les problèmes d'équilibre, l'algorithme de l'extragradient et autres méthodes de projection

  • Sandy VAUTRON

    Student thesis: Master typesMaster in Mathematics

    Abstract

    The aim of this work is to study an equilibrium problem in the sense of Blum and Oettli. This problem is very general and contains, as particular cases, the optimization problem, the variational inequality problem, the Nash equilibrium problem in noncooperative games, the fixed point problem and the nonlinear complementarity problem. We study various numerical methods for solving the equilibrium problem. First, we start with the auxiliary equilibrium problem principle. Then, we consider projection methods using an exact propjection on the most violated constraint, an axtragradient algorithm, and a subgradient method. Finally we develop the case where the constraint set is a set of fixed points. For each method, we give the corresponding algorithm and we study its convergence.
    Date of Award2009
    Original languageFrench
    SupervisorJean-Jacques Strodiot (Supervisor), Van Hien Nguyen (Jury) & Joseph Winkin (Jury)

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