Colloquium à 10h45

Oratrice : Irène Waldspurger (Paris-Dauphine)

Titre : Low-rank optimization

Résumé : A low-rank optimization problem is a problem where one must minimize a function over the set of matrices, and the minimizer happens (or is constrained) to be low rank: its rank is much smaller than its number of lines or columns. I will introduce and motivate these problems. Then, I will explain the difficulties which arise when trying to numerically solve them, and the possible algorithmic approaches. I will in particular describe the so-called Burer-Monteiro factorization, and the theoretical as well as numerical questions it raises.