Optimisation II

Description

Objectifs

At the end of this module, the student will have understood and be able to explain (main concepts):

- Deterministic differentiable optimisation :
Existence and unicity of optimisation problems, KKT points, Convergence of optimization algorithm, Lagrangian duality

- Discrete stochastic optimisation :
The Metropolis-Hastings algorithm, the simulated annealing algorithm, genetic algorithms.

The student will be able:
- To identify families of optimization problems
- To choose and implement suitable first and second order algorithms
- To implement a Metropolis-Hastings algorithm in order to simulate, approximately, a given discrete probability distribution on a huge finite space.
- To implement a simulated annealing algorithm in order to minimize a given function on a huge finite space.

Pré-requis

Optimisation I
Markov chains and applications

Évaluation

L’évaluation des acquis d’apprentissage est réalisée en continu tout le long du semestre. En fonction des enseignements, elle peut prendre différentes formes : examen écrit, oral, compte-rendu, rapport écrit, évaluation par les pairs…