Optimization

Description and scopes

Optimization is a research field at the confluence of mathematics, computer science and economics, whose importance is growing in part because of its many applications to socio-economic problems. The aim of the Optimization program is to provide students with a broad expertise in mathematical optimization and related topics, including game theory and optimal control. 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. 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. The following topics are covered :

  • Optimal control and dynamic programming, both deterministic and stochastic ;
  • Game theory and its applications ;
  • Calculus of variations and optimal transport ;
  • Stochastic optimization ;
  • Advanced optimization algorithms ;
  • Operation research (in collaboration with the MPRO program).

Contact and practical information

Board: Quentin Mérigot (Université Paris-Saclay, Director), Pierre Carpentier (ENSTA), Stéphane Gaubert (Polytechnique), Jean-Chrisophe Pesquet (CentraleSupélec).

Administrative assistant: Séverine Simon

Language and venue: All courses proposed by our program are given in English, but courses by partner programs (e.g. MPRO) might be in French. Most of the courses are held in the campus of Institut Polytechnique de Paris (Polytechnique and ENSTA, Palaiseau), and at Université Paris-Saclay (Orsay).

Organization of the year 2021-2022 :

  • Welcome meeting : September 7 at 5pm in Orsay (room 2L8).
  • Intensive training courses : August 30 to September 10 in Institut de mathématique d'Orsay: Functional analysis (Matthieu Léautaud) and Optimization (Rémy Rodia)
  • Basic courses : September 13 to November 12 (holidays: october 25-29).
  • Advanced courses : November 15 to January 28 (holidays: december 17 to January 3).
  • The second term starts on January 31.
  • The program will end on September 30, 2022.

Structure of the studies

First term

Basic courses (mid-September to mid-November)

  • Convex analysis and optimization (Quentin Mérigot and Jean-Christophe Pesquet)
  • Game theory (Bruno Ziliotto)
  • Introduction to operations research and combinatorics (Céline Gicquel and Xavier Allamigeon)
  • Optimal control of ODEs (Frédéric Bonnans and Laurent Pfeiffer)
  • Dynamic programming (Marianne Akian)

Advanced courses (mid-November to mid-January)

  • Advanced game theory and applications (Olivier Beaude and Samson Lasaulce)
  • Calculus of variations (Jean-François Babadjian)
  • Derivative-free optimization (Anne Auger and Laurent Dumas)
  • Stochatic optimization (Olivier Fercoq and Vincent Leclère)
  • Zero-sum dynamic games (Stéphane Gaubert)
  • Optimization project

External courses:

  • Elliptic PDEs (Frédéric Rousset), from M2 AMS
  • Optimization in graphs, from MPRO
  • Complexity theory, from MPRO
  • Mathematical programming, from MPRO

Information about specific courses: MPRO courses are in French. The schedule is available here. French as a foreign language (FLE) courses, the information should be here.

Second term

Specialized courses (January to march)

  • Dynamic of information and communication in games (Tristan Tomala), from MiE
  • Geometric control (Dario Prandi)
  • Numerical PDEs for image processing (Jean-Marie Mirebeau), from MVA
  • Optimal transport (Yann Brenier and Luca Nenna)
  • Optimization and statistics (Francis Bach), from StatML
  • Invited course on Mean-field games, by François Delarue

Internship (3 to 6 months)

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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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