Filter-trust-region methods for nonlinear optimization

    Student thesis: Doc typesDoctor of Sciences

    Abstract

    This work is concerned with the theoretical study and the implementation of algorithms for solving two particular types of nonlinear optimization problems, namely unconstrained and simple-bound constrained optimization problems. For unconstrained optimization, we develop a new algorithm which uses a filter technique and a trust-region method in order to enforce global convergence and to improve the efficiency of traditional approaches. We also analyze the effect of approximate first and second derivatives on the performance of the filter-trust-region algorithm. We next extend our algorithm to simple-bound constrained optimization problems by combining these ideas with a gradient-projection method. Numerical results follow the proposed methods and indicate that they are competitive with more classical trust-region algorithms.
    Date of Award17 Apr 2007
    Original languageEnglish
    Awarding Institution
    • University of Namur
    SupervisorPhilippe TOINT (Supervisor), N. I. M. Gould (Jury), Luis VICENTE (Jury), Annick Sartenaer (Jury) & Jean-Jacques STRODIOT (Jury)

    Keywords

    • Filter methods
    • Trust-region methods
    • Nonlinear programming

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