Volume 56, Number 5, September-October 2022
|Page(s)||1629 - 1653|
|Published online||20 July 2022|
Energy-adaptive Riemannian optimization on the Stiefel manifold
Institute of Mathematics, University of Augsburg, Universitätsstr. 12a, 86159 Augsburg, Germany
2 Institute of Mathematics & Centre for Advanced Analytics and Predictive Sciences (CAAPS), University of Augsburg, Universitätsstr. 12a, 86159 Augsburg, Germany
* Corresponding author: firstname.lastname@example.org
Accepted: 8 April 2022
This paper addresses the numerical solution of nonlinear eigenvector problems such as the Gross–Pitaevskii and Kohn–Sham equation arising in computational physics and chemistry. These problems characterize critical points of energy minimization problems on the infinite-dimensional Stiefel manifold. To efficiently compute minimizers, we propose a novel Riemannian gradient descent method induced by an energy-adaptive metric. Quantified convergence of the methods is established under suitable assumptions on the underlying problem. A non-monotone line search and the inexact evaluation of Riemannian gradients substantially improve the overall efficiency of the method. Numerical experiments illustrate the performance of the method and demonstrates its competitiveness with well-established schemes.
Mathematics Subject Classification: 65N25 / 81Q10
Key words: Riemannian optimization / Stiefel manifold / Kohn–Sham model / Gross–Pitaevskii eigenvalue problem / nonlinear eigenvector problem
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.