Institut Polytechnique de Paris
Ecole Polytechnique ENSTA ENSAE Télécom Paris Télécom SudParis

Master Year 2 Optimization

Master Year 2 Optimization
Year

Master Year 2

Program

Optimization

ECTS Credits

60

Language

English

Orientation

Industry and Research

Location

Palaiseau Campus, Université Paris-Saclay 

Course duration

12 months, full time

Course start

September

Degree awarded

Master’s degree

WHY ENROLL IN THIS PROGRAM?

Asset n° 1 

Acquire high-level knowledge with a comprehensive program covering all aspects of optimization and its interfaces (control, games, and operations research)

Asset n°2

Access the growing number optimization-related career opportunities in companies and research

Asset n°3

Choose to complete an internship or research project in an academic department or industry

The Optimization Master’s program covers all aspects of optimization, paying special attention to areas specific to the research context of the Saclay Plateau.

The diverse range of topics studied includes optimal control (discrete and continuous time, deterministic and stochastic), game theory, variational calculus (optimization in analysis and partial differential equations), stochastic optimization and stochastic optimization methods, and operational research. Many of the courses are pooled with the IT Master’s program, in particular, Operational Research courses are borrowed from the MPRO program.

The Year 2 Master prepares students for both academic and industrial research, and to become mathematical engineers. Companies are actively looking for candidates with knowledge and experience of optimization, as shown by EDF’s involvement in the Gaspard Monge Program for Optimization (PGMO). PGMO supports this Master by funding the lectures given by international experts.

Objectives

This program enables students to:

  • Acquire broad expertise in mathematical optimization and related topics including game theory, optimal control and calculus of variations
  • Cover a wide range of topics including:
    • Optimal control and dynamic programming (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
  • The main career openings for optimization graduates are in applied research with large research bodies (CNRS, CEA, CNES, INRIA, INRA, INSERM) or the R&D centers of big companies like EDF, Air-France, Orange, SNCF, Engie, Dassault, Thalès, Bouygues/LocalSolver, ...), or of research oriented SMEs in the field of Operations Resarch and Optimization (Artelys, Eurodecision,…)
  • Most students engage in a PhD program either in an industrial or academic laboratory
  • In recent years, SMEs and innovative startups in the digital world, in France and abroad, are increasingly looking for this kind of profile

The first two weeks of September are devoted to optional training courses, granting no credits :

  • Functional Analysis
  • Numerical Analysis / programming
  • Basic Optimization
  • Probability

During the first term, 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.

During the second term, students are expected to validate 2 specialized courses or one selected external course.

They 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).

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

Basic courses (September-November)

Convex Analysis and Optimization

30h

5 ECTS

English

Optimal Control of ODEs

30h

5 ECTS

English

Introduction to Operational Research and Combinatorics

30h

5 ECTS

English

Dynamical Programming

30h

5 ECTS

English

Game theory

30h

5 ECTS

English

Advanced courses (November-January)

Advanced Continuous Optimization

30h

5 ECTS

English

Calculus of Variations

30h

5 ECTS

English

Derivative-Free Optimization

30h

5 ECTS

English

Stochastic Optimization

30h

5 ECTS

English

Advanced game theory and applications

30h

5 ECTS

English

Tropical and Operator methods for zero-sum repeated games

30h

5 ECTS

English

Selected courses from partner programs

Complexity theory

24h

4 ECTS

English

Optimization in graphs

24h

4 ECTS

English

Mathematical programming

30h

5 ECTS

English

Elliptic partial differential equations

30h

5 ECTS

English

Sequential Learning, Sequential Optimization

30h

5 ECTS

English

Seminars

Seminars

12h

2 ECTS

English

Optimal Transport

18h

3 ECTS

English

Geometric control

18h

3 ECTS

English

Optimal Control of PDEs

18h

3 ECTS

English

Dynamics of information and communication in games

18h

3 ECTS

English

Optimization and Statistics (invited course)

18h

3 ECTS

English

Advanced Continuous Optimization, II

18h

3 ECTS

English

PGMO (Invited course)

18h

3 ECTS

English

Seminars

12h

2 ECTS

English

French as a foreign language

12h

2 ECTS

English

Research internships (20 ECTS) take place between April and August, in laboratories (academic or industrial).

 

Research laboratories from Institut Polytechnique de Paris and Paris-Saclay with academics teaching in the Master

  • CMAP : CNRS, INRIA & Ecole Polytechnique
  • LIX : CNRS, INRIA & Ecole Polytechnique
  • PREG-CECO : CNRS & Ecole Polytechnique
  • UMA : CNRS, INRIA & ENSTA Paris
  • GREGHEC : CNRS & HEC Paris
  • IMO : CNRS & Université Paris-Saclay
  • LRI : CNRS & Université Paris-Saclay
  • CentraleSupelec
  • Laboratoire de Mathématiques de Versailles (UVSQ)

Admission requirements

Academic prerequisites

Completion of the first year of Master in mathematics at Institut Polytechnique de Paris or equivalent in France (engineering school) or abroad. The program requires a strong background in mathematics, but computer scientists and economists also participate in the training of the students.

Language prerequisites

English

How to apply

Applications can be submitted exclusively online. You will need to provide the following documents:

  • Transcript
  • Two academic references (added online directly by your referees)
  • CV/resume
  • Statement of purpose

You will receive an answer in your candidate space within 2 months of the closing date for the application session.

Fees and scholarships

  • EU/EEA/Switzerland students: 243€
  • Non-EU/EEA/Switzerland students: 3770€
  • Engineer students enrolled in one of the five member schools of Institut Polytechnique de Paris (Ecole polytechnique, ENSTA Paris, ENSAE Paris, Télécom Paris and Télécom SudParis): 159€
  • Special cases: please refer to the "Cost of studies" section of the FAQs

Find out more about scholarships

Applications and admission dates

Coordinators

  • Coordinator for Institut Polytechnique de Paris: Stéphane Gaubert (Institut Polytechnique de Paris and INRIA)
  • General coordinator: Quentin Mérigot (IMO, Université Paris-Saclay)

Other academic contacts

Program office

Nicoletta Bourgeois

General enquiries

master-admission@ip-paris.fr

Description

The Optimization Master’s program covers all aspects of optimization, paying special attention to areas specific to the research context of the Saclay Plateau.

The diverse range of topics studied includes optimal control (discrete and continuous time, deterministic and stochastic), game theory, variational calculus (optimization in analysis and partial differential equations), stochastic optimization and stochastic optimization methods, and operational research. Many of the courses are pooled with the IT Master’s program, in particular, Operational Research courses are borrowed from the MPRO program.

The Year 2 Master prepares students for both academic and industrial research, and to become mathematical engineers. Companies are actively looking for candidates with knowledge and experience of optimization, as shown by EDF’s involvement in the Gaspard Monge Program for Optimization (PGMO). PGMO supports this Master by funding the lectures given by international experts.

Objectives

This program enables students to:

  • Acquire broad expertise in mathematical optimization and related topics including game theory, optimal control and calculus of variations
  • Cover a wide range of topics including:
    • Optimal control and dynamic programming (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
  • The main career openings for optimization graduates are in applied research with large research bodies (CNRS, CEA, CNES, INRIA, INRA, INSERM) or the R&D centers of big companies like EDF, Air-France, Orange, SNCF, Engie, Dassault, Thalès, Bouygues/LocalSolver, ...), or of research oriented SMEs in the field of Operations Resarch and Optimization (Artelys, Eurodecision,…)
  • Most students engage in a PhD program either in an industrial or academic laboratory
  • In recent years, SMEs and innovative startups in the digital world, in France and abroad, are increasingly looking for this kind of profile

The first two weeks of September are devoted to optional training courses, granting no credits :

  • Functional Analysis
  • Numerical Analysis / programming
  • Basic Optimization
  • Probability

During the first term, 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.

During the second term, students are expected to validate 2 specialized courses or one selected external course.

They 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).

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

Basic courses (September-November)

Convex Analysis and Optimization

30h

5 ECTS

English

Optimal Control of ODEs

30h

5 ECTS

English

Introduction to Operational Research and Combinatorics

30h

5 ECTS

English

Dynamical Programming

30h

5 ECTS

English

Game theory

30h

5 ECTS

English

Advanced courses (November-January)

Advanced Continuous Optimization

30h

5 ECTS

English

Calculus of Variations

30h

5 ECTS

English

Derivative-Free Optimization

30h

5 ECTS

English

Stochastic Optimization

30h

5 ECTS

English

Advanced game theory and applications

30h

5 ECTS

English

Tropical and Operator methods for zero-sum repeated games

30h

5 ECTS

English

Selected courses from partner programs

Complexity theory

24h

4 ECTS

English

Optimization in graphs

24h

4 ECTS

English

Mathematical programming

30h

5 ECTS

English

Elliptic partial differential equations

30h

5 ECTS

English

Sequential Learning, Sequential Optimization

30h

5 ECTS

English

Seminars

Seminars

12h

2 ECTS

English

Optimal Transport

18h

3 ECTS

English

Geometric control

18h

3 ECTS

English

Optimal Control of PDEs

18h

3 ECTS

English

Dynamics of information and communication in games

18h

3 ECTS

English

Optimization and Statistics (invited course)

18h

3 ECTS

English

Advanced Continuous Optimization, II

18h

3 ECTS

English

PGMO (Invited course)

18h

3 ECTS

English

Seminars

12h

2 ECTS

English

French as a foreign language

12h

2 ECTS

English

Research internships (20 ECTS) take place between April and August, in laboratories (academic or industrial).

 

Research laboratories from Institut Polytechnique de Paris and Paris-Saclay with academics teaching in the Master

  • CMAP : CNRS, INRIA & Ecole Polytechnique
  • LIX : CNRS, INRIA & Ecole Polytechnique
  • PREG-CECO : CNRS & Ecole Polytechnique
  • UMA : CNRS, INRIA & ENSTA Paris
  • GREGHEC : CNRS & HEC Paris
  • IMO : CNRS & Université Paris-Saclay
  • LRI : CNRS & Université Paris-Saclay
  • CentraleSupelec
  • Laboratoire de Mathématiques de Versailles (UVSQ)

Admission requirements

Academic prerequisites

Completion of the first year of Master in mathematics at Institut Polytechnique de Paris or equivalent in France (engineering school) or abroad. The program requires a strong background in mathematics, but computer scientists and economists also participate in the training of the students.

Language prerequisites

English

How to apply

Applications can be submitted exclusively online. You will need to provide the following documents:

  • Transcript
  • Two academic references (added online directly by your referees)
  • CV/resume
  • Statement of purpose

You will receive an answer in your candidate space within 2 months of the closing date for the application session.

Fees and scholarships

  • EU/EEA/Switzerland students: 243€
  • Non-EU/EEA/Switzerland students: 3770€
  • Engineer students enrolled in one of the five member schools of Institut Polytechnique de Paris (Ecole polytechnique, ENSTA Paris, ENSAE Paris, Télécom Paris and Télécom SudParis): 159€
  • Special cases: please refer to the "Cost of studies" section of the FAQs

Find out more about scholarships

Applications and admission dates

Coordinators

  • Coordinator for Institut Polytechnique de Paris: Stéphane Gaubert (Institut Polytechnique de Paris and INRIA)
  • General coordinator: Quentin Mérigot (IMO, Université Paris-Saclay)

Other academic contacts

Program office

Nicoletta Bourgeois

General enquiries

master-admission@ip-paris.fr