Principe du problème auxiliaire et méthoddes de projection pour la résolution de problèmes d'équilibre

  • Marie-Paule Castelain

Student thesis: Master typesMaster in Mathematics

Abstract

We consider equilibrium problems which include variational inequalities, Nash equilibria in noncooperative games, vector optimization and complementarity problems for instances. We study a method to solve equilibrium problems based on the fixed point formulation. We present a slight modification of the previous algorithm which considers a line search. We show that such problems are particular instances of convex feasibility problems with infinitely many convex sets. To solve these problems, we use projection algorithms for convex feasibility. There can be modified in order to improve their convergence properties mainly achieving global convergence. We present a projection algorithm with a most violated constraint control strategy. And finally we show a variante of the previous algorithm using approximate projections instead of exact ones. We include full convergence analysis of these algorithms.
Date of Award2007
Original languageFrench
SupervisorJean-Jacques Strodiot (Supervisor), Van Hien Nguyen (Jury) & Geneviève Salmon (Jury)

Cite this

Principe du problème auxiliaire et méthoddes de projection pour la résolution de problèmes d'équilibre
Castelain, M. (Author). 2007

Student thesis: Master typesMaster in Mathematics