TY - JOUR
T1 - Accelerated Optimization with Orthogonality Constraints
AU - Siegel , Jonathan W.
JO - Journal of Computational Mathematics
VL - 2
SP - 207
EP - 226
PY - 2020
DA - 2020/11
SN - 39
DO - http://doi.org/10.4208/jcm.1911-m2018-0242
UR - https://global-sci.org/intro/article_detail/jcm/18372.html
KW - Riemannian optimization, Stiefel manifold, Accelerated gradient descent, Eigenvector problems, Electronic structure calculations.
AB - <p style="text-align: justify;">We develop a generalization of Nesterov&#39;s accelerated gradient descent method which
is designed to deal with orthogonality constraints. To demonstrate the effectiveness of
our method, we perform numerical experiments which demonstrate that the number of
iterations scales with the square root of the condition number, and also compare with
existing state-of-the-art quasi-Newton methods on the Stiefel manifold. Our experiments
show that our method outperforms existing state-of-the-art quasi-Newton methods on some
large, ill-conditioned problems.</p>