Précédent : Références Remonter : Projet PROMATH

Abstract

This project is devoted to the study of Mathematical Programming - or numerical optimization - from the theoretical and practical viewpoints, as well as its application to problems of industrial origin. This includes: the theory of optimality conditions, stability of optimal solutions with respect to parameters, the construction of optimization algorithms, their application to concrete problems. We consider that our work has three components:

Basic research which can be motivated by advanced applications, or by ongoing work among the international scientific community.

Development of optimization algorithms, aimed at solving large classes of emerging problems, rather than particular instances of applications.

Applications This means the collaboration with industrial partners (or coming from other research areas) on specific problems they are faced with.

Naturally, these three domains are not independent: each one is constantly nourrished by the other two. This year, our main results concerned

- the theory of optimization: sensitivity analysis and 2nd-order development, particularly in semi-definite programming, optimal control, decomposition of large-scale problems, variational inequalities ;

- algorithmic development: interior-point and quasi-Newton methods, line-searches, decomposition ;

- applications: car industry, optics, telecommunications, metallurgy, optimal control, electrical production.

Among the main events of this year, we mention the implementation of one of our optimization codes by the European Center for Medium Range Meteorological Forecast (Reading, England) for their daily prevision; Meteo France is doing the same. Besides, Renault has decided to adopt our methodology for automatic gas injection.