Energy-adaptive Riemannian optimization on the Stiefel manifold
A talk in the BI.discrete Workshop series by
Daniel Peterseim from Augsburg
| Abstract: | This talk addresses the numerical simulation 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 method 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. Numerical experiments illustrate the performance of the method and demonstrate its competitiveness with established schemes. (joint work with: R. Altmann and T. Stykel, reference: https://arxiv.org/abs/2108.09831). Attendance is only possible after registration with the organizers and with 3G-certificate. Within the CRC this talk is associated to the project(s): A7, B7 |