Optimization

Ects : 6

Enseignant responsable :

Volume horaire : 58.5

Description du contenu de l'enseignement :

The course focuses on finite-dimensional optimization problems and their numerical resolution.

  • Basic concepts: existence of optimisers; optimality conditions; convexity and strict convexity.
  • Unconstrained optimisation: gradient descent (principles, convex case, extensions); Newton’s method; numerical implementations.
  • Constrained optimisation: Lagrange multipliers for equality and inequality constraints; KKT conditions; numerical methods; duality.
  • Introduction to optimal control: discrete-time problems, dynamic programming principle and Bellman equations. Possible brief outlook toward calculus of variations and continuous-time optimal control.

Pré-requis recommandés :

Optimisation dans R^n sans contraintes.

Compétence à acquérir :

Finite-dimensional optimization problems and their numerical resolution.

Mode de contrôle des connaissances :

Examen sur table (mi-semestre et fin de semestre).