News

Kohn–Sham type problems form the computational core of density functional theory and give rise to large-scale, nonlinear eigenvalue problems whose accurate and efficient solution remains a central challenge in electronic structure calculations. In this talk, we provide an overview of energy-adaptive Riemannian optimization strategies for the numerical solution of Kohn–Sham type equations. This includes theoretical foundations like construction of the energy-adaptive metric for the different Riemannian manifolds, practical aspects like the gradient calculation and general choice of parameters, and challenges and limitation of energy-adaptive approaches. The talk concludes with an illustration of practical performance in numerical experiments.