Optimization on manifolds to solve low-rank
Nicolas Boumal, Princeton
Optimization on manifolds is about minimizing a cost
function over a smooth manifold, such as spheres, low-rank
matrices, orthonormal frames, rotations, etc. I will present the
basic framework as well as some of the more general convergence
results, including recent complexity results. (Toolbox: http://www.manopt.org
This is non-convex optimization; there are no global
optimality guarantees in general. Nevertheless, I will discuss a
class of problems related to semidefinite relaxations for
Max-Cut and community detection in the stochastic block model
for which standard optimization algorithms on manifolds converge
to global optimizers. This is part of a growing set of
applications on manifolds with stronger theoretical backup.
Joint work with P.-A. Absil, A. Bandeira, C. Cartis
and V. Voroninski.