Lectures on optimization methods
- Introduction. Convex sets and cones
- Dual cone. Convex functions
- Convex optimization problems
- KKT optimality conditions and intro to duality
- Conic duality intro
- Packages for solving convex optimization problems + DCP and ipopt demo
- Introduction to numerical optimization. Gradient descent and lower bounds concept
- Beyond gradient descent: heavy ball, conjugate gradient and fast gradient methods
- Stochastic first-order methods
- Newton and quasi-Newton methods
- Projected gradient method, Frank-Wolfe method and introduction to proximal methods
- Linear programming problem
- Semidefinite programming
- Interior point methods and concept of self-concordance functions