Descriptif

This course will cover the fundamentals of convex optimization with a strong focus on finite dimensional search spaces. It covers theory, algorithm and applications.

The syllabus contains: convex sets,  convex functions, optimization problems, subdifferential calculus (subgradients), optimality conditions in convex or differentiable optimization with equality and inequality constraints, duality theory. The last part is an introduction to the optimal control of ordinary differential equations.

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.