Program and courses

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 :PDF (the document is still the one for 2017/18).

Intensive training courses

Approx 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 MA and MathSV)
  • Statistics (C. Kéribin, U. Paris-Sud, common with MA and MathSV)
First-term courses

Basic courses (September to November)

Each course is credited 5 ECTS and lasts approx 30h. The list of teachers has been updated for 2018/19.

  • 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, C. Gicquel U. Paris-Sud, D. Quadri, U. Paris-Sud)
  • Dynamical Programming (M. Akian, INRIA, and J.-P. Chancelier, ENPC, common with ENSTA)
  • Game Theory (V. Perchet, ENS Paris-Saclay, with MVA)

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 C. Sagastizabal)
  • Calculus of Variations (J.-F. Babadjian, 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 (P. Carpentier, ENSTA, V. Leclère Ecole des Ponts)
  • Dynamic games (G. Vigeral, Paris-Dauphine, T. Tomala HEC)

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, 3 ECTS)
  • Optimization in Graphs (from MPRO, 5 ECTS)
  • Mathematical Programming (from MPRO, 5 ECTS)
  • Elliptic PDEs (from AMS, 5 ECTS)
Second-term courses

Specialized Courses

  • 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 (F. Bonnans INRIA, with AMS)
  • Dynamics of information and communication in games ( T. Tomala, HEC, with the Economics Master program)

Invited course : A. Shapiro (Georgia Tech., details to be announced)

Courses from other programs

  • Optimization and Statistics (F. Bach, INRIA, from MA)
  • Sequential Learning, Sequential Optimization (G. Stoltz, HEC, from MA)
  • Foundations of distributed and large-scale computing optimization (J.-C. Pesquet Centrale-Supélec and E. Chouzenoux Paris-Est, from MVA)

This year a specialized course offered by Ecole Polytechnique can be validated fro the second term, but is actually held during the first

Description Nonsmoothness (...)

Description
Nonsmoothness prevails optimization in most of its theoretical and practical aspects. Even if the starting point is a smooth (or even a polynomial) model, natural operations like marginal/value functions, min/max selections etc destroy smoothness. In addition, extrema of nonsmooth functions occur, in general, at points of nondifferentiability. This has inevitably led to the development of the modern variational analysis and of nonsmooth optimization algorithms. Since the seminal example of Weierstrauss, back to 1872, exhibiting a univariate continuous real-valued function which is nowhere differentiable, it has been commonly understood that pathologies are tightly linked with almost all theories in classical analysis. Variational Analysis, handling nonsmooth objects cannot be an exception. Notwithstanding, in most applications nonsmoothness arises together with an intrinsic structure : for instance, an initial polynomial model will give rise to a semialgebraic structure. Therefiore, although a general nonsmooth theory will be full of pathological situations, it is founded to consider the trace of this theory within well-behaved paradigms. This course aims at underlining the use of these paradigms in optimization, focusing in minimization algorithms or general descent systems. After an introductory crash course in Nonsmooth Analysis, we shall consider Nonsmooth Optimization problems enjoying a nice intrinsic structure : The Tame paradigm —which is what is nowadays called Tame Optimization encompassing the semialgebraic structures— and the (classical) Convex paradigm. Convergence analysis of the proximal algorithm —a central tool in nonsmooth minimization— will be presented in the light of these two paradigms, emphasizing important convergence properties. So far, some of these properties seem to be eluded even in the convex case. Relations between continuous vs discrete dynamical descent systems will be presented. A secondary aim of this course is to provide essential background and material for further research. During the lectures, some open problems will be eventually mentioned.

Students who do not have French as their native language will be proposed a French course (2 ECTS).

Seminars

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 :

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 :