**Objective**: The optimization theory is a pleasant mathematical framework within which it is possible to interpret, in the same terms, most problems of optimum control, identification, numerical analysis, statistics, mechanics and economics.

Objective

To acquire the common related bases for modelling, studying and controlling complex systems.

Traditionally, a model, which is the first step towards a quantitative and qualitative analysis of a system, is made up of state variables (position and moment of a particle, reserves of rare resources, a magnitude measuring or conserving the memory of a system) and control of variables (force fields, buying or selling, decisions influencing the state of the system).

The variables are interlinked through static constraints (admissible bounds on the states or controls, factory production limits) or dynamic ones (evolution equations, taken from physics, in mechanical engineering or robotics, for example). A criterion to optimize could be an energy (dislocation energy, kinetic energy), a cost (investment or management costs), a preferential relation, a satisfaction index, a length (problem of the shortest route), a distance versus a desired state of the system (target to reach), a time period or any other magnitude that can be influenced by control variables.

**Programme**:

- free optimization and optimization under constraints in finite dimensions;
- dynamic optimization;
- methods for optimizing large systems.

**Last Modification :**Sunday 12 December 2010