Optimization underpins many engineering problems, where we are tasked with modeling 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. Optimization is also very present in everybody's life when one tries to ``optimize'' 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 and convex continuous optimization in finite dimensions. We will leave out discrete optimization (often referred to as Operations Research), and infinitely dimensional optimization (such as shape optimization).

We will focus on theoretical aspects, the algorithmic ones being left for the follow-up course OPT202.

The goal of this course is to

• To learn what optimization is (what problems are solved and how, what are the basic assumptions, e.g., convexity, and how to interpret the output of an optimization problem)
• To understand the basic optimization models (convex, non-convex, etc..) and know how to formulate an optimization problem that makes sense
• To understand that optimization 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 course OPT202 (by Andrea Simonetto) will dig a little deeper into both algorithms and practice.

All the available course materials will be available in Moodle. Because the course is offered for the first time in this form, no lecture notes are available yet. 

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