Optimisation multiniveaux en norme infinie et critères d'arrêt associés

  • Mélodie Mouffe

    Student thesis: Doc typesDoctor of Sciences

    Abstract

    This thesis presentation concerns the study of a multilevel trust-region algorithm in infinity norm, designed for the solution of nonlinear optimization problems of high size, possibly submitted to bound-constraints. The multilevel algorithm that we study has been developed on the basis of the algorithm created by Gratton, Sartenaer and Toint (2008). In this work, we look at both theoretical and numerical properties of the new algorithm. In a first part, the main features of the new algorithm are exposed. We then look at several stopping criteria for nonlinear bound-constrained optimization algorithms. In particular we define stopping criteria that are meaningful in terms of backward error analysis. We finally compare numerically our method to competing algorithms in the same field in order to show its remarkable efficiency.
    Date of Award10 Feb 2009
    Original languageFrench
    Awarding Institution
    • University of Namur
    SupervisorPhilippe TOINT (Co-Supervisor), Serge Gratton (Co-Supervisor), IS Duff (Jury), M Kocvara (Jury), F Glineur (Jury) & ANNICK SARTENAER (President)

    Keywords

    • backward error
    • convergence theory
    • bound constraints
    • trust-region methods
    • nonconvex optimization
    • Multilevel optimization
    • stopping criteria

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