Energy-adaptive Riemannian optimization on the Stiefel manifold

DOI10.1051/m2an/2022036zbMath1502.65177arXiv2108.09831OpenAlexW3196167832WikidataQ115334313 ScholiaQ115334313MaRDI QIDQ5038945

Tatjana Stykel, Daniel Peterseim, Robert Altmann

Publication date: 9 October 2022

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.09831

zbMATH Keywords

Stiefel manifoldRiemannian optimizationKohn-Sham modelGross-Pitaevskii eigenvalue problemnonlinear eigenvector problem

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) NLS equations (nonlinear Schrödinger equations) (35Q55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Computational density functional analysis in statistical mechanics (82M36) PDE constrained optimization (numerical aspects) (49M41)

Related Items (4)

On the Convergence of Sobolev Gradient Flow for the Gross–Pitaevskii Eigenvalue Problem ⋮ The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem ⋮ On Optimal Convergence Rates for Discrete Minimizers of the Gross–Pitaevskii Energy in Localized Orthogonal Decomposition Spaces ⋮ Slow and finite-time relaxations to \(m\)-bipartite consensus on the Stiefel manifold

Uses Software

• KSSOLV

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A feasible method for optimization with orthogonality constraints
• Geodesics in infinite dimensional Stiefel and Grassmann manifolds
• A perturbation-method-based post-processing for the planewave discretization of Kohn-Sham models
• Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations
• Parameterised local spin density exchange-correlation energies and potentials for electronic structure calculations. I: Zero temperature formalism
• The \(J\)-method for the Gross-Pitaevskii eigenvalue problem
• Exponential convergence of Sobolev gradient descent for a class of nonlinear eigenproblems
• Implicit algorithms for eigenvector nonlinearities
• Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation
• A brief introduction to manifold optimization
• Cholesky QR-based retraction on the generalized Stiefel manifold
• A constrained optimization algorithm for total energy minimization in electronic structure calculations
• Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models
• Projection-like Retractions on Matrix Manifolds
• KSSOLV—a MATLAB toolbox for solving the Kohn-Sham equations
• Computational chemistry from the perspective of numerical analysis
• Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure
• Preconditioned gradient flows for nonlinear eigenvalue problems and application to the Hartree-Fock functional
• The Geometry of Algorithms with Orthogonality Constraints
• On the convergence of SCF algorithms for the Hartree-Fock equations
• Empirical Arithmetic Averaging Over the Compact Stiefel Manifold
• A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
• Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
• Localization and Delocalization of Ground States of Bose--Einstein Condensates Under Disorder
• Sobolev Gradient Flow for the Gross--Pitaevskii Eigenvalue Problem: Global Convergence and Computational Efficiency
• Localized Computation of Eigenstates of Random Schrödinger Operators
• Convergence Analysis of Direct Minimization and Self-Consistent Iterations
• Finite Elements
• A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas

This page was built for publication: Energy-adaptive Riemannian optimization on the Stiefel manifold