Minimisation de fonctions polynomiales par l'utilisation de sommes de carrés

Abstract

We are interested in global unconstrained minimization of polynomial functions in many variables. A part of the study will show how semidefinite programming permits to transform a polynomial into a sum of squares and how these techniques of sum of squares can be used to minimize a polynomial. Thereafter, we will develop some notions of algebraic-geometry to end at the "Positivstellensatz". We will then analyse the programs of the SOSTOOLS toolbox that are utilized for the minimization and the determination of a sum of squares decomposition of a polynomial. Wi will show how the different elements of the theory take place in it, this as well in terms of semidefinite programming as in terms of the "Positivstellensatz". We will conclude by using these programs for different polynomials.

Date of Award	2005
Original language	French
Supervisor	Philippe TOINT (Supervisor), Annick Sartenaer (Jury) & Joseph Winkin (Jury)