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Optimisation

Responsable : Filippo Santambrogio, Université Paris-Sud
Responsable à l'Ecole Polytechnique : Stéphane Gaubert

This master program will provide students with a broad expertise in Mathematical Optimization and related topics, and will train them for academic and industrial research, or for Mathematical Engineering jobs after high-level studies in a strongly research-oriented environment. The program provides a wide, integrated, multi-disciplinary training in optimization, covering continuous, combinatorial, and stochastic aspects, with a special attention to those topics which are specific to the research of Paris-Saclay.

The main tracks of the program concern :
- Advanced algorithms for continuous optimization in convex and non-convex frameworks;
- Stochastic optimization and stochastic methods for optimization;
- Optimal control (dynamic programming in continuous and discrete time, in the deterministic and stochastic settings);
- Game theory, its connections with between optimization and its applications;
- Calculus of variations and other applications of mathematical analysis to advanced optimization problems, in particular shape optimization;
- Operational research. Students will be offered the opportunity to follow MPRO lectures on Combinatorial Optimization.

Even if this program is indeed a master in applied mathematics, both computer scientists and economists can participate in the training. Interdisciplinary courses at the interface of mathematics, computer science and economics will be an important part of the program.

Prerequisites: 4 years of studies in mathematics and engineering school with strong mathematical background.
Structure: Two weeks of intensive training courses (no grades, just freshening up main notions): September
1st term:  6 courses of 30h each (chosen among 10 + exterior and partner courses). From September to January.
2nd term: 2 specialized courses of 20h each (among 6 + exterior and partner courses). February-March.
During the year: students attend research and applied seminars on different aspects of mathematical optimization.
Second term: internship or research project in a laboratory, in academics, or in private or public companies - approximately between April-August. Public defense of the research report produced during the internship research project: between July and September.

Careers
PhDs in academic or industrial laboratories leading to academic or industrial careers, or immediate hiring in R&D departments. Most large French companies employ experts in optimization, and sometimes have dedicated research groups in optimization and operational research (eg. Air France, Air Liquide, Bouygues, EDF, GDF SUEZ, Orange, SNCF...) A number of small companies also offer services in optimization.

VOIR AUSSI : la majeure "Contrôle, Optimisation, Calcul des Variations" (COCV) du master Mathématiques de la Modélisation.