Optimization algorithms on the Grassmann manifold

Sato Hiroyuki

29th October (Fri) 13:30

In this talk, discussed are several optimization algorithms on the Grassmann manifold.
First, a brief review of several optimization algorithms in Euclidean space is given, e.g. steepest descent method, Newton's method, and trust-region method. And then, these methods are generalized to those on Riemannian manifolds.
What we have studied are optimization algorithms on the Grassmann manifold. We view the Grassmann manifold as a set of all projection matrices with a certain rank, which characterizes the size of the Grassmann manifold. Finally, Application of optimization algorithms to problems on the Grassmann manifold will be shown.