École Nationale Supérieure de
Techniques Avancées

Abstract

This document sums up the first part of the design of a nonsmooth optimization algorithm in order to solve problems resulting from the complementarity field. Constructing such an algorithm, having robustness and global convergence in mind, proved to be more complex than expected, with many subtle difficulties and technical points arising. Multiple details are given concerning the encountered hindrances, such as obtaining an adequate Gauss- Newtonian model, ensuring a descent direction, globalizing with the Levenberg-Morrison-Marquardt method... Linear problems, which are overall easier being a particular case, are given specific attention throughout the document, allowing to go further deeper in the analysis. Though there are no numerical experiments, they are one of the goal of this project : they could not be done due to lack of time. Many elements are not finished yet, thus we present the most advanced notions and what are the ideas we will work on.