Optimisation

Optimization

Description: In this course, students are expected to acquire and master various fundamental aspects of continuous optimization. The following concepts will be covered and implemented in practice: formulation of optimization problems, conditions for the existence of global and local minimizers, convexity, duality, Lagrange multipliers, first-order methods, linear programming. The use of differentiable programming will be presented in practical work. Stochastic gradient-free methods, such as CMAES and PSO, will also be covered.

Learning outcomes: By the end of this course, students will master the fundamental concepts of continuous optimization (conditions for the existence of global and local minimizers, convexity, duality, Lagrange multipliers, first-order methods, linear programming, stochastic methods).

Evaluation methods: 1h written test, can be retaken

Evaluated skills:

  • Modelling
  • Research and Development

Course supervisor: Michel Barret

Geode ID: SPM-MAT-004

CM:

  1. Bases de l’optimisation 1/2 (1.5 h)
  2. Bases de l’optimisation 2/2 (1.5 h)
  3. Convexité, quelques algorithmes itératifs (1.5 h)
  4. Dualité (1.5 h)
  5. Programmation linéaire (1.5 h)
  6. Méthode des multiplicateurs de Lagrange (1.5 h)
  7. Méthodes stochastiques gradient-free (1.5 h)

TD:

  1. Dualité (1.5 h)
  2. Programmation linéaire (1.5 h)
  3. Méthode des multiplicateurs de Lagrange (1.5 h)

TP:

  1. Bases de l’optimisation (3.0 h)
  2. Convexité, quelques algorithmes itératifs (3.0 h)
  3. Méthodes stochastiques gradient-free (3.0 h)