Optimization

 Description and Scopes

The aim of master program is to provide students with a broad expertise in mathematical optimization and related topics, including game theory, optimal control, calculus of variations, etc. After this program, students can either pursue in PhD, or be hired as a mathematical engineer in the R&D department of a company. About 70% of our Alumni started a PhD thesis (academic or industrial) after following our program. The Alumni and previous internships page gives more information.

This program requires a strong background in mathematics, but computer scientists and economists will also participate in the training of the students. The following topics are covered, among others :

  • Optimal control and dynamic programing, both deterministic and stochastic ;
  • Game theory and its applications in economics and learning ;
  • Calculus of variations, at the interface of optimization and PDEs ;
  • Stochastic optimization ;
  • Operation research (in collaboration with the MPRO program) ;
  • Advanced optimization algorithms.

Board of the program : Q. Mérigot, Univ. Paris-Sud (Director) ; P. Carpentier, ENSTA ; S. Gaubert, INRIA and École Polytechnique ; J.-C. Pesquet, Centrale-Supélec ; T. Tomala, HEC
Language : All courses proposed by our program are given in English. On the other hand, external courses (from other programs) are not guaranteed to be in English.
Venue : Most of the courses are held in the campus of Polytechnique-ENSTA (Palaiseau), and at Université Paris-Sud (Orsay). Some courses are elsewhere : Centrale-Supélec, ENS Paris-Saclay, ENSAE.

 Structure of the studies

Courses start in early September and finish early-April. A research internship lasting at least 3 months is required, and the duration can go up to 6 months.

First term (September-January, 30 ECTS)

The first two weeks of september are devoted to optional training courses, granting no credits : Functional Analysis (D. Le Peutrec, U. Paris-Sud), Numerical Analysis / programming (J.-B. Apoung Kamga, U. Paris-Sud), Basic Optimization (B. Buet, U. Paris-Sud), Probability (C. Graham, Polytechnique). The students are expected to validate 30 credits from basic courses (September-November), advanced courses (November-January) and from a few selected courses from partner programs.

First term courses
Advanced Continuous Optimization 1 J.-C. Gilbert (INRIA) 5 ECTS Basic
Optimal Control of ODEs F. Bonnans (Inria) and H. Zidani (ENSTA) 5 ECTS Basic
Introduction to Operational Research and Combinatorics X. Allamigeon (Inria/Polytechnique), C. Gicquel (U. Paris-Sud), D. Quadri (U. Paris-Sud) 5 ECTS Basic
Dynamical Programming M. Akian (Inria) and J.-P. Chancelier (ENPC) 5 ECTS Basic
Game theory, algorithms and learning V. Perchet (ENS Paris-Saclay) 5 ECTS Basic
Advanced Continuous Optimization II J.-C. Gilbert (Inria) 5 ECTS Advanced
Calculus of Variations J.-F. Babadjian (U. Paris-Sud) 5 ECTS Advanced
Derivative-Free Optimization A. Auger (Inria/Paris-Sud), and L. Dumas (U. Versailles) 5 ECTS Advanced
Stochastic Optimization P. Carpentier (ENSTA), V. Leclère (Ecole des Ponts) 5 ECTS Advanced
Dynamic games G. Vigeral (Paris-Dauphine), T. Tomala, (HEC) 5 ECTS Advanced
Complexity theory Olivier Hudry (Télécom ParisTech) 3 ECTS Mutualized (MPRO)
Optimization in graphs Christophe Picouleau (CNAM), Cédric Bentz (CNAM) 5 ECTS Mutualized (MPRO)
Mathematical programming Sourour Elloumi (ENSTA), Alain Faye (ENSIIE), Axel Parmentier (ENPC/CERMICS) 5 ECTS Mutualized (MPRO)
Elliptic partial differential equations Jean-François Babadjian (U. Paris-Sud) 5 ECTS Mutualized (AMS)


Second term (February-August, 30 ECTS)

Students are expected to validate 2 specialized courses or one selected external course. In addition, we validate credits for

  • Seminars : attending research and applied seminars on the different sides of mathematical optimization throughout the year, and writing a short report.
  • Invited course given by a prominent researcher of the field, followed by students but also by researchers.
  • Internship : In addition, students must do an internship or research project, either in an academic department or in industry. This should last between 3 and 6 months, usually between April and August. Requirements include a research report and an oral defense (usually done in the first half of September, but defenses can be arranged in July, if needed).
Second term courses
Optimal Transport Q. Mérigot (U. Paris-Sud) 4 ECTS Specialized
Geometric control Y. Chitour (U. Paris-Sud), F. Jean (ENSTA) and D. Prandi (CNRS/U. Paris-Sud) 4 ECTS Specialized
Tropical Algebra in Games and Optimization S. Gaubert (Inria/Polytechnique) 4 ECTS Specialized
Optimal Control of PDEs F.Bonnans (Inria) 4 ECTS Specialized
Dynamics of information and communication in games T. Tomala (HEC) 4 ECTS Specialized
Invited course A. Shapiro (Georgia Tech) 2 ECTS
Seminars 2 ECTS
Internship 20 ECTS
Optimization and Statistics F. Bach, INRIA 4 ECTS Mutualized (MA)
Sequential Learning, Sequential Optimization G. Stoltz (HEC) 4 ECTS Mutualized (MA)
Foundations of distributed and large-scale computing optimization J.-C. Pesquet Centrale-Supélec and E. Chouzenoux Paris-Est 4 ECTS Mutualized (MVA)

 Admission and scholarships

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.

To apply , please visit the Paris-Saclay platform devoted to the master in Mathematics and Applications.

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. Pay attention that 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 way in advance.

Scholarships

A number of scholarships are available for excellent students wishing to attend this master program. Warning : admission to the master program and obtention of a scholarship are two different, and independent issues. Being admitted to the program does not imply that you will receive a scholarship.

  • FMJH : Students can apply to the scholarships of Fondation Hadamard.
  • IDEX Paris-Saclay : Université Paris-Saclay also offers master scholarships as well. The procedure is the following : the selection committee of the Optimization program will propose a few candidates to an IDEX scholarship. If this happens to you, you will be asked to complete your application and ask for some recommendation letters.