M2 Optimization: Description and scope
Optimization is a research field at the confluence of mathematics, computer science and economics. Its importance is growing, in part, because of its many applications to socio-economic problems. The aim of M2 Optimization to provide students with a broad expertise in mathematical optimization and related topics:
- Optimal control ;
- Game theory ;
- Optimal transport and calculus of variations;
- Computational optimization and operation research ;
- Stochastic aspects of optimisation, control, etc.
Most of our Alumni started a PhD thesis (academic or industrial) after following our program, others are hired as mathematical engineer in the R&D department of a company.
Courses
| First semester | ||
| Basic courses | Convex analysis and optimization | Q. Mérigot, Orsay J.-C. Pesquet, CentraleSupélec |
| Game theory | B. Ziliotto, CNRS/Dauphine | |
| Introduction to operations research and combinatorics | C. Gicquel, Orsay X. Allamigeon, Inria/Polytechnique |
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| Optimal control of ODEs | F. Bonnans, Inria/CentraleSupélec L. Pfeiffer, Inria/CentraleSupélec |
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| Dynamic programming | M. Akian, Inria/Polytechnique | |
| Advanced courses | Advanced game theory and applications | O. Beaude, EDF S. Lasaulce, CNRS/CRAN |
| Calculus of variations | J.F. Babadjian, Orsay | |
| Derivative-free optimization | A. Auger, Inria/Polytechnique L. Dumas, Versailles |
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| Stochatic optimization | O. Fercoq, Télécom V. Leclère, Ponts ParisTech |
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| Zero-sum dynamic games | S. Gaubert, Inria/Polytechnique | |
| External courses | Elliptic PDEs | F. Rousset, Orsay |
| Optimization in graphs | MPRO | |
| Complexity theory, | MPRO | |
| Mathematical programming | MPRO | |
| Second semester | ||
| Specialized courses | Dynamic of information and communication in games | T. Tomala, HEC |
| Geometric Control | D. Prandi, CNRS/CentraleSupélec | |
| Numerical PDEs for image processing | J.-M. Mirebeau, CNRS/ENS PSaclay | |
| Optimal transport | Y. Brennier, CNRS/Orsay L. Nenna, Orsay |
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| Optimisation and statistics | F. Bach, Inria Paris A. Dieuleveut, Polytechnique |
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| Optimal control of PDEs | F. Bonnans | |
| PGMO Invited course | PGMO | |
| Internship: 3 to 6 month in an academic or industrial research lab | ||
The 2021/22 PGMO invited course is given by François Delarue:
More information
This program requires a strong background in mathematics (typically 4 years of university studies), but a significant portion of the courses offered are shared with other master programs in mathematics, computer science, economics. In particular, operations research (OR) courses are offered thanks to a collaboration with the MPRO program.
- Language: All courses proposed by our program are given in English. Courses by partner programs might be in French.
- Venue: Université Paris-Saclay (Orsay) and Institut Polytechnique de Paris (Palaiseau).
- Board: Quentin Mérigot (UPSaclay, Director), Sorin-Mihai Grad (ENSTA), Stéphane Gaubert (Polytechnique), Jean-Christophe Pesquet (CentraleSupélec).
- Administrative assistant: Séverine Simon
Admission
Admission to this master program is based on previous academic results, through transcripts and recommandation letters. The typical prerequisites to be admitted to the master program include 4 years of studies in mathematics and/or engineering schools with strong mathematical background.
Foreign students. European students can enroll in the same way as French students do. Students from outside Europe may need a visa and have to take care of their immigration issues as soon as possible. Students coming from a list of countries need to pass through Campus France in order to prepare their visa application, and this may require to start the procedure long in advance.
Scholarships. A number of scholarships are available for excellent students wishing to attend this master program. Note that being admitted to the program does not imply that you will receive a scholarship. French and foreign students can apply to the scholarships of the Fondation Hadamard. Université Paris-Saclay also offers master scholarships as well, to foreign students. If you apply early enough (before mid-april), the admission jury of the Optimization program may select you as a candidate to an IDEX scholarship. If this happens to you, you will be asked to complete your application and ask for some recommendation letters. More details can be found on this page.
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