Descriptif
Prerequisite: MAA202
MAA307 is composed of three connected parts. The first one lays the foundation of convex analysis in Hilbert spaces, and covers topics such as: convex sets, projection, separation, convex cones, convex functions, Legendre-Fenchel transform, subdifferential. The second part deals with optimality conditions in convex or
differentiable optimization with equality and inequality constraints, and opens the way to duality theory and related algorithms (Uzawa, augmented Lagrangian, decomposition and coordination). The last part is an introduction to the optimal control of ordinary differential equations.
MAA307 complements MAA209 on the theoretical side, but MAA209 is not mandatory.
Diplôme(s) concerné(s)
Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique
Vous devez avoir validé l'équation suivante : UE MAA202
Format des notes
Numérique sur 20Littérale/grade américainPour les étudiants du diplôme Echanges PEI
Le rattrapage est autorisé (Note de rattrapage conservée écrêtée à une note seuil de 10)- Crédits ECTS acquis : 4 ECTS
La note obtenue rentre dans le calcul de votre GPA.
Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique
Le rattrapage est autorisé (Note de rattrapage conservée écrêtée à une note seuil de 10)- Crédits ECTS acquis : 4 ECTS
La note obtenue rentre dans le calcul de votre GPA.
Programme détaillé
- Convex sets (convex combinations, convex hull, projection and separation, cones)
- Convex functions (including indicator and support functions, lower semicontinuity, closed convex hull, Legendre-Fenchel transform)
- Optimization without explicit constraint (existence issues, elements of subdifferential calculus, parametric duality)
- Optimality conditions with equality and inequality constraints (KKT conditions in convex or differentiable optimization)
- Lagrangian duality and algorithmic notions (proximal and projection methods, Lagrangian duality, Uzawa's algorithm, augmented Lagrangian, decomposition and coordination)
- Introduction to the optimal control of ordinary differential equations (adjoint method, Lagrangian, Hamiltonian, Pontryagin's principle, Riccati's equation and feedback law)
Support pédagogique multimédia
