# Lectures

Hand-written lecture notes:

20.10.Lecture 1Chapter I: Introduction
22.10.Lecture 2Chapter II: Minimizing a convex function
27.10.Lecture 3Chapter III: Conic Optimization
§1 Convex cones
29.10Lecture 4§2 The PSD cone
3.11Lecture 5§3 Conic programs
5.11Lecture 6§4 Theorem of alternatives
10.11Lecture 7
12.11Lecture 8§5 Duality theory
17.11Lecture 9Chapter IV: First applications
§1 Robust optimization
19.11Lecture 10§2 Eigenvalue optimization
24.11Lecture 11§3 SDP relaxations of quadratic programs
Chapter V: Approximation algorithms
§1 MAX CUT
26.11Lecture 12
1.12Lecture 13
3.12Lecture 14§2 Eigenvalue interpretation of the SDP relaxation for MAX CUT
§3 Little Grothendieck inequality / Nesterov's approximation algorithm
8.12Lecture 15§4 Grothendieck's inequality
10.12Lecture 16Chapter VI: Determinant Maximization
§1 Convex spectral functions
15.12Lecture 17§2 MAXDET optimization
17.12Lecture 18
22.12Lecture 19§3 Approximation of polytopes by ellipsoids
7.1Lecture 20
12.1Lecture 21
14.1Lecture 22Chapter VII: Packings and colorings in graphs
§1 Basic definitions
§2 Semidefinite relexation for $\alpha$ and $\chi$
19.1Lecture 23§3 Perfect Graphs
21.1Lecture 24
26.1Lecture 25§4 Shannon capacity
28.1Lecture 26
2.2Lecture 27Chapter VIII: Copositive Programming
§1 The completely positive and the copositive cone
4.2Lecture 28§2 A copositive reformulation of the independence number of a graph
9.2Lecture 29Chapter IX: Polynomial Optimization
§1 Nonnegative polynomials and sum of squares
11.2 (fällt aus)Lecture 30§2 Global optimization with polynomials