Riemannian optimization methods for nonlinear eigenvector problems

Thursday, December 1st, 2022
5 p.m., on Zoom

In this talk, we address the numerical solution of nonlinear eigenvector problems arising in computational physics and chemistry. These problems characterize critical points of the underlying energy function on the infinite-dimensional Stiefel manifold. To efficiently compute energy minimizers, we propose a novel Riemannian gradient descent method induced by an energy-adaptive metric.  The 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.
(Joint work with R. Altmann and D. Peterseim)