Component
École Nationale Supérieure d'Électrotechnique d'Électronique d'Informatique d'Hydraulique et des Télécommunications
Objectives
- By the end of this course, students will have learned how to formulate a constrained optimization problem with a view to solving it.
- They will be able to describe the problem in terms of an objective function under constraints and use numerical tools to solve it optimally.
Description
- Illustration of design problems formalized as optimization problems with constraints.
- Review of unconstrained optimization: mathematical theorems and gradient algorithms, optimal step gradient, Newton and quasi-Newton.
- Optimization with constraints on variables: first simple projection algorithm.
- Mathematical formalization of optimization problems with constraints.
- Presentation of Penalty Methods
- Definition of the Lagrange Function
- KKT Theorem (Karush-Khun-Tucker)
- Uzawa Algorithm, Active-set, SQP, Interior Point Algorithm