Optimization methods, Department of Innovation and High Technologies, Fall 2021

Lectures on optimization methods

Syllabus

1. Introduction. Convex sets and cones
2. Dual cone. Convex functions
3. Convex optimization problems
4. KKT optimality conditions and intro to duality
5. Conic duality intro
6. Packages for solving convex optimization problems + DCP and ipopt demo
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. Linear programming problem
13. Semidefinite programming
14. Interior point methods and concept of self-concordance functions