Polynomial Optimization: Theory and Applications

This lecture covers topics in polynomial optimization, focusing on the theory and applications of sum-of-squares polynomials. It discusses the challenges of checking nonnegativity in polynomials and presents the Hilbert theorem on SOS polynomials. The instructor explains the concept of monomials and demonstrates how any polynomial can be represented as a quadratic function of monomials. The session concludes with the theorem stating the conditions for a polynomial to be SOS. Practical examples and proofs are provided throughout the lecture.