# Convex Optimization and Optimal Control

Prerequisites:

• Topology and multivariable calculus (MAA202 or equivalent) is mandatory.
• Measure and integration (MAA301, MAA310 or equivalent) is useful for the fully rigorous understanding of the last part (optimal control), but it is not strictly mandatory. All the notions needed for the exercises and the exam will be reminded.

MAA307 is composed of three connected parts. The first one lays the foundation of convex analysis in Hilbert spaces, and covers topics such as: convex sets, projection, separation, convex cones, convex functions, Legendre-Fenchel transform, subdifferential. The second part deals with optimality conditions in convex or differentiable optimization with equality and inequality constraints, and opens the way to duality theory and related algorithms. The last part is an introduction to the optimal control of ordinary differential equations and discusses, in particular, the concepts of adjoint state, Hamiltonian and feedback law.

MAA307 complements MAA209 on the theoretical side, but MAA209 is not mandatory.

Prerequisite: MAA202
Convex Optimization and Optimal Control is composed of three connected parts. The first one lays the foundation of convex analysis in Hilbert spaces, and covers topics such as: convex sets, projection, separation, convex cones, convex functions, Legendre-Fenchel transform, subdifferential. The second part deals with optimality conditions in convex or differentiable optimization with equality and inequality constraints, and opens the way to duality theory and related algorithms. The last part is an introduction to the optimal control of ordinary differential equations and discusses, in particular, the concepts of adjoint state, Hamiltonian and feedback law.