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 + Stable set problem)
- Lecture 10: Nonnegative polynomials on the real line
- Lecture 11: Nonnegative polynomials on the real line (continued)
- Lecture 12: Nonnegative polynomials on the real line (continued)
- Lecture 13: Nonnegative multivariate polynomials
- Lecture 14: Sum of squares hierarchies and Positivstellensatz
- Lecture 15: Sum of squares on the hypercube
- Lecture 16: Sum of squares on the hypercube (continued)

If you find any mistake or typos in the lecture notes please let me know by email at: h.fawzi [AT] damtp DOT cam DOT ac.uk

- Our first example class will be Tuesday 17/10 at 15h00 in MR4. We will go through the exercises of Lecture 2. Solution sheet.
- Example class 2: Tuesday 31/10 at 16h00 in MR5. Exercise sheet. Solution sheet.
- Example class 3: Tuesday 21/11 at 15h00 in MR14. Exercise sheet. Solution sheet.