Appears in collection : 2023 - T3 - WS2 - Special Week

The aim of these tutorial lectures is to introduce the mathematical background of the moment-sums of squares (SOS) hierarchy approach to polynomial optimization. Polynomial optimization consists of minimizing a polynomial of many real variables subject to polynomial equality and inequality constraints. The moment-SOS hierarchy is an approach to polynomial optimization that solves it globally at the price of solving a family of convex optimization problems of increasing size.