Optimisation underpins many engineering problems, where we are tasked with modelling and finding the optimal decision in a variety of contexts. Take as an example, the optimal control of an autonomous vehicle that has to navigate street constraints, or the optimal training of neural networks. Optimisation is also very present in everybody's life, when one try to ``optimise'' their agenda to fit all their activities and still find time to study for the exams.

In this course, we are going to present key concepts and results in differentiable continuous optimisation in finite dimension, which is a very broad area in optimisation. We will leave out discrete optimisation (which is often referred to as Operations research), and infinite dimension optimisation (such as shape optimisation).

We will focus on theoretical aspects as well as algorithmic, and we will show how they are related.

The goal of the course is to

• To learn what is optimisation (what problems are solved and how, what are the basic assumption, e.g., convexity, and how to interpret the output of an optimisation problem)
• To understand the basic optimisation models (convex, non-convex, etc..) and know how to formulate an optimisation problem that makes sense
• To acquire the basic lingo and properties of optimisation algorithms, so that one is able to tell why, when something doesn’t work in practice.
• To understand that optimisation is math (so without theorems one doesn’t go very far), but also computations (scaling is important), and engineering (models, models, models).

The course is the first of two: the follow up OPT202 will dig a little deeper in both theory and practice, especially when the simplyfing assumptions of the OPT201 (e.g., differentiability) don't hold anymore.

All the materials will be available in Moodle

Remarque: ce cours compte pour 3 ECTs pour l'obtention du M1-Mathématiques Appliquées