Max-Cut Problem: SDP Relaxation and Randomized Rounding

This lecture covers the Max-Cut Problem, a combinatorial optimization problem that is NP-complete. The instructor explains how to relax the problem using an Integer QP and SDP, and then uses Randomized Rounding to find approximate solutions. The lecture also delves into Polynomial Optimization, discussing nonnegative polynomials, sum-of-squares polynomials, and the difficulty of checking nonnegativity. Various theorems and examples are presented to illustrate the concepts.