Structure of the studies
Students must collect 60 ECTS (credits) to validate the program.
First term (September-January)
- Intensive training courses : two weeks in September (no grades and no ECTS, it is just to freshen up the main notions).
- Basic and advanced courses : students must typically choose 6 courses of 30h each (from a list of 10 courses offered by the master program, plus exterior and partner courses). Basic courses run from September to November, advanced courses from November to January. Most courses are credited 5 ECTS.
Second term (February-August)
- Specialized courses : students must choose two courses of approx. 20h each (from a choice of six, plus exterior, invited and partner courses). They run from February to March-April and are typically credited 4 ECTS.
- Seminars : students can attend research and applied seminars on the different sides of mathematical optimization throughout the year. This can give 2 ECTS.
- Stage : students must do an internship or research project in a laboratory (in academical institutions, or in private or public companies, under the supervision of a professor). This is credited 20 ECTS and should last between 3 and 6 months, usually between April and August.
- Public defense : the research report produced during the internship will be defended in order to validate the master. This is usually done in the first half of September (but defenses can be arranged in July, if needed).
List of courses
Detailed programs and descriptions of the courses can be found here :
Intensive training courses
15h each course. These courses are not compulsory, and have no exam at the end. Their content will be considered as a basis for starting the master program.
- Functional Analysis (D. Le Peutrec, U. Paris-Sud, common with AMS)
- Numerical Analysis / programming (J.-B. Apoung Kamga, U. Paris-Sud, common with AMS)
- Basic Optimization (B. Buet, U. Paris-Sud)
- Probability (C. Graham, Polytechnique, common with ALEA and MathSV)
Basic courses (September to November)
Each course is credited 5 ECTS and lasts approx 30h.
- Advanced Continuous Optimization I (J.-C. Gilbert, INRIA)
- Optimal Control of ODEs (F. Bonnans, INRIA, and H. Zidani, ENSTA, common with AMS and with ENSTA)
- Introduction to Operational Research and Combinatorics (X. Allamigeon, INRIA and Polytechnique, and C. Gicquel and D. Quadri, U. Paris-Sud)
- Dynamical Programming (M. Akian, INRIA, and J.-P. Chancelier, ENPC, common with ENSTA)
- Game Theory (T. Tomala, HEC)
Advanced courses (November to January)
Each course is credited 5 ECTS and lasts approx 30h.
- Advanced Continuous Optimization II (J.-C. Gilbert, INRIA ; this course will also feature an invited advanced course by M. Teboulle, U. Tel Aviv)
- Calculus of Variations (F. Santambrogio, U. Paris-Sud, common with AMS)
- Derivative-Free Optimization (A. Auger, INRIA and Paris-Sud, and L. Dumas, U. Versailles, common with AMS)
- Stochastic Optimization (F. Bonnans, INRIA, and P. Carpentier, ENSTA)
- Dynamic games (V. Perchet, ENS Cachan, R. Laraki, CNRS and Polytechnique, common with OJD)
Students can also choose the following courses from partner programs (the value in ECTS of each course depends on the duration) :
- Complexity Theory (from MPRO)
- Optimization in Graphs (from MPRO)
- Mathematical Programming (from MPRO)
- Elliptic PDEs (F. Rousset, U. Paris-Sud, from AMS)
- Optimal Transport (Q. Mérigot U. Paris-Sud, with AMS)
- Geometric Control (U. Boscain, CNRS and Polytechnique, Y. Chitour, U. Paris-Sud, and F. Jean, ENSTA, with AMS)
- Tropical Algebra in Games and Optimization (S. Gaubert, INRIA and Polytechnique, with COCV)
- Optimal Control of PDEs (A. Kroener, INRIA, with AMS)
- Sequential Learning, Sequential Optimization (G. Stoltz, HEC, with MA)
- Advanced Game Theory ( T. Tomala, HEC, with the Economics Master program)
Invited course : C. Daskalakis (MIT) will give a course on algorithmic game theory, 10h.
Courses from other programs
- Optimization and Statistics (F. Bach, INRIA, from MA)
- Information transmission, communication in games (J. Hagenbach, CNRS and Polytechnique, from the Economics Master program).
Students who do not have French as their native language will be proposed a French course (2 ECTS).
Students are encouraged to participate in the seminars related to optimisation of Paris-Saclay and the Paris region. Adequate participation (certified by the teachers of the master program and confirmed by a short dissertation on some of the topics of the seminars) will give 2 ECTS. We propose the following seminars :
- Séminaire Parisien d’Optimisation (Monday afternoon, once per month)
- Séminaire Parisien de Théorie des Jeux (Monday morning, weekly)
- GT de Calcul des Variations (Monday morning, once every 3 weeks)
- PGMO seminar (variable dates)
- Conférences industrielles du MPRO
- Other seminars organized during the year.
Students can also propose seminars that they find by their own means (contact the Director of the program for acceptance). To be informed about seminars, several mailing lists exist, essentially one for each of the cycles presented above. Also look at this other page.
Partner programs :
- MPRO, Master Parisien de Recherche Opérationnelle (Operational Research)
- AMS, Analyse Modélisation Simulation (PDE and Scientific Computing)
- MA, Mathématique de l’Aléatoire (Probability and Statistics)
- FIIL, Fondements de l’Informatique et Ingénierie du Logiciel (Computer Science)
- COCV, Contrôle, Optimisation, Calcul des Variations (part of the modeling master program at Paris 6)