Trust-region algorithms for derivative-free optimization and nonlinear bilevel programming

Abstract

This work is concerned with the design and the implementation of algorithms for solving two particular types of optimization problems, namely derivative-free optimization problems and nonlinear bilevel programs. In the first case we are interested in problems where the cost for evaluating the objective function is very expensive and its derivatives are not available while the second class is characterized by problems involving two mathematical programs, the solution of one being part of the constraints of the other. For both cases, the algorithms we present are iterative procedures and at each step they construct a model of the original problem and solve it within a trust region. The presentation of these algorithms is followed by a series of numerical results tending to confirm the promising behavior of the methods.

Date of Award	2003
Original language	English
Supervisor	Philippe Toint (Supervisor), Jacques HENRARD (Jury), Annick Sartenaer (Jury), Gilles Savard (Jury) & Luis VICENTE (Jury)