Summary
International Symposium on Nonlinear Theory and its Applications
2005
Session Number:2-1-5
Session:
Number:2-1-5-5
A Note on Riemannian Optimization Methods on the Stiefel and the Grassmann Manifolds
Yasunori Nishimori,
pp.349-352
Publication Date:2005/10/18
Online ISSN:2188-5079
Summary:
We prove the updating rules given by the Riemannian optimization methods on the Stiefel and the Grassmann manifolds coincide if the target function for optimization on the Stiefel manifold has a symmetry so that it is regarded as a function on the Grassmann manifold. The Grassmann condition is encapsulated in this symmetry. Therefore we do not need the formulas for the Grassmann manifold separately; all of them, the natural gradient method, the conjugate gradient method, and the Newton method reduce to the counterparts for the Stiefel manifold.