Optimization methods, Department of Innovation and High Technologies

Lectures on optimization methods and applications

• Fall 2021
• Fall 2022

Syllabus

1. Introduction. Convex sets and cones
2. Dual cone. Automatic differentiation. JAX demo
3. Convex functions
4. Convex optimization problems
5. KKT optimality conditions and intro to duality
6. Conic duality intro
7. Introduction to numerical optimization. Gradient descent and lower bounds concept
8. Beyond gradient descent: heavy ball, conjugate gradient and fast gradient methods
9. Stochastic first-order methods
10. Newton and quasi-Newton methods
11. Projected gradient method, Frank-Wolfe method and introduction to proximal methods
12. Semidefinite programming
13. Packages for solving convex optimization problems + DCP and ipopt demo