Year: 2021
Author: Jonathan W. Siegel
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 2 : pp. 207–226
Abstract
We develop a generalization of Nesterov'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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1911-m2018-0242
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 2 : pp. 207–226
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Riemannian optimization Stiefel manifold Accelerated gradient descent Eigenvector problems Electronic structure calculations.
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