Course description

- A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization (SIAM).
- G. Blekherman, P. A. Parrilo, R. R. Thomas (editors), Semidefinite Optimization and Convex Algebraic Geometry (SIAM).
- S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press.

- Lecture 1: Review of convexity (separating hyperplane theorem, faces and extreme points, Minkowski theorem)
- Lecture 2: Review of convexity (continued) (convex cones, dual cones)
- Lecture 3: The positive semidefinite cone
- Lecture 4: Conic programming
- Lecture 5: Semidefinite programming (definition and first examples)
- Lecture 6: Duality in conic programming (1)
- Lecture 7: Duality in conic programming (2) (Strong duality theorem)
- Lecture 8: Binary quadratic optimisation (1) (Max cut)
- Lecture 9: Binary quadratic optimisation (2) (Max cut - continued)
- Lecture 10: Maximum stable set problem and LovĂˇsz theta number
- Lecture 11: Nonnegative polynomials on the real line
- Lecture 12: Nonnegative polynomials on the real line (continued)
- Lecture 13: Nonnegative polynomials on the real line and the moment problem
- Lecture 14: Nonnegative multivariate polynomials
- Lecture 15: Sum-of-squares hierarchies
- Lecture 16: Constrained polynomial optimisation: the case of the hypercube

- Our first example class will be Tuesday 31/01 at 15h00 in MR4. We will go through the exercises of Lecture 2. Solution sheet.
- Example class 2: Tuesday 7/02 at 15h00 in MR4. We will go through Exercise 3.2 of Lecture 3. Solution sheet.
- Example class 3: Tuesday 14/02 at 15h00 in MR4. We will go through the exercises of Lecture 7. Solution sheet.
- Example class 4: Tuesday 7/03 at 15h00 in MR4. We will go through the exercises of Lectures 11,12,13. Solution sheet.
- Revision class: The revision class will be Thursday May 4th 14:00-16:00 in MR4. Click here for the exercises sheet. Solution sheet