Boaz Barak is teaching a sister seminar in parallel at Harvard/MIT.
In this graduate seminar we cover recent research results on the use of mathematical programming for problems arising from optimization, machine learning, computational complexity and more. A particular focus is on the Parrilo–Lasserre “Sum of Squares” semidefinite programming hierarchy. We discuss both lower and upper bounds, as well as how such mathematical programs give rise to a general theory of computational difficulty, computation vs. sample size tradeoffs, and computational analogs of Bayesian probabilities.