Efficacité et fiabilité des méthodes utilisant l’approche ‘Branch-and-Bound‘ pour l’optimisation globale non convexe

Abstract

In the first part of this thesis, we study some unconstrained multidimensional global optimization methods using the Branch-and-Bound technique. This study improves the efficiency and reliability of these methods and determines the classes of problems for which they would be effective. The goal of the second part is to present and implement a new approach of global optimization, based on the reduction of the dimension. It involves the Alienor reducing transformation method which uses α-dense curves. The feasible domain in this part is defined from the non-linear constrained.