Optimization

This course provides a solid presentation of modern convex analysis and convex optimization algorithms for large scale problems. Topics include: Ekeland's variational principle, subdifferential calculus, duality and Fenchel-Legendre transform, projection on a closed convex set, proximal operators and Moreau's regularization, accelerated and optimal first-order methods, Hopf/Lax-Oleinik representation formulas for Hamilton-Jacobi equations. The course will provide the mathematical and algorithmic underpinnings. It will also explore some applications in signal and image processing, optimal control and machine learning.