Une combinaison des méthodes de recherche linéaire et de région de confiance dans le cadre de l'optimisation non-linéaire sans contraintes

Abstract

Concerning this thesis, we propose an algorithm for unconstrained nonlinear optimization that employs both line search and trust region techniques. Unlike a traditional line search Newton-CG method, also known as the truncated Newton method, our algorithm permits to exploit directions of negative curvature. If such a direction is encountered, instead of stopping the conjugate gradient, we follow this direction inside of a safeguarded trust region which is updated at each iteration. We have implemented this new algorithm in Fortran 77 and compared it with a classical line search Newton-CG method. In fact, we tested the algorithm on a set of 166 problems from the CUTEr collection and the numerical results are presented in the last chapter.

Date of Award	2004
Original language	French
Supervisor	Annick Sartenaer (Supervisor), Jean-Jacques Strodiot (Jury) & Philippe Toint (Jury)