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.
More information can be found on the following website : https://www.master-in-optimization.fr
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
Registration fees are available here
Find out more about scholarships
Please note that fees and scholarships may change for the following year.
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
- Pierre Carpentier (ENSTA Paris)
- Sorin-Mihai Grad (ENSTA Paris)
Program office
General enquiries
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.
More information can be found on the following website : https://www.master-in-optimization.fr
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
Registration fees are available here
Find out more about scholarships
Please note that fees and scholarships may change for the following year.
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
- Pierre Carpentier (ENSTA Paris)
- Sorin-Mihai Grad (ENSTA Paris)