Semester | Mand. | Option | Filières |
x | |||
MA1, MA3 | x | C | |
MA1, MA3 | x | D E | |
MA1 | x |
Lecture | 2 weekly |
Exercises | 2 weekly |
Study plan | Semester | Mand. | Option | Filières |
EDMT - Management of Technology 2019-20 | x | |||
Energy Science and Technology 2019-2020 | MA1 | x | ||
Génie électrique et électronique 2019-20 | MA1 | x | D E | |
Génie électrique et électronique 2019-20 | MA3 | x | D E | |
Management, technologie et entrepreneuriat 2019-20 | MA1 | x | C | |
Management, technologie et entrepreneuriat 2019-20 | MA3 | x | C |
Cursus | Sem. | Type |
---|---|---|
Electrical and Electronical Engineering | MA1, MA3 | Obl. |
Energy Science and Technology | MA1 | Obl. |
Management of technology | Obl. | |
Managmt, tech et entr. | MA1, MA3 | Opt. |
Convex optimization is a fundamental branch of applied mathematics that has applications in almost all areas of engineering, the basic sciences and economics. For example, it is not possible to fully understand support vector machines in statistical learning, nodal pricing in electricity markets, the fundamental welfare theorems in economics, or Nash equilibria in two-player zero-sum games without understanding the duality theory of convex optimization.
The course primarily focuses on techniques for formulating decision problems as convex optimization models that can be solved with existing software tools. The exact formulation of an optimization model often determines whether the model can be solved within seconds or only within days, and whether it can be solved for ten variables or up to 10^6 variables. The course does not address optimization algorithms but covers the theory that is necessary to follow advanced courses on algorithm design such as EE-556: Mathematics of data: from theory to computation.
Tentative Course Outline:
Week 1: Introduction / Convex Sets
Week 2: Convex Sets / Convex Functions
Week 3: Convex Functions / Convex Optimization Problems
Week 4: Convex Optimization Problems
Week 5: Introduction to Duality Theory
Week 6: Optimality Conditions / Separation Theorems
Week 7: Strong Duality
Week 8: Optimization in Statistics and Machine Learning
Week 9: Optimization in Statistics and Machine Learning
Week 10: Convexifying Nonconvex Problems
Week 11: Convexifying Nonconvex Problems
Week 12: Robust Optimization
Week 13: Robust Optimization
Week 14: Stochastic Programming
Students are assumed to have good knowledge of linear algebra and analysis.
Some familiarity with linear programming or other optimization paradigms is useful but not necessary. Students are expected to be familiar with the MATLAB programming environment.
Classical formal teaching interlaced with practical exercices and computational courseworks.
Midterm Exam (30%, covering weeks 1-7)
2 MATLAB-based Courseworks (20%, covering weeks 8-14)
Final Exam (50%, covering weeks 1-14)
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
obligatoire
obligatoire
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
obligatoire
obligatoire
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
obligatoire
obligatoire
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
obligatoire
obligatoire
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
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