Direct minimization of electronic structure calculations with Householder reflections

We consider a minimization scheme based on the Householder transport operator for the Grassman manifold, where a point on the manifold is represented by a m x n matrix with orthonormal columns. In particular, we consider the case where m >> n and present a method with asymptotic complexity mn^...

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Bibliographic Details
Published in:arXiv.org 2012-07
Main Authors: Baarman, K, Eirola, T, Havu, V
Format: Article
Language:English
Subjects:
Asymptotic methods
Columns (structural)
Conjugate gradient method
Conjugates
Electronic structure
Manifolds
Nonlinear programming
Operators (mathematics)
Optimization
Parameterization
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Summary:We consider a minimization scheme based on the Householder transport operator for the Grassman manifold, where a point on the manifold is represented by a m x n matrix with orthonormal columns. In particular, we consider the case where m >> n and present a method with asymptotic complexity mn^2. To avoid explicit parametrization of the manifold we use Householder transforms to move on the manifold, and present a formulation for simultaneous Householder reflections for S-orthonormal columns. We compare a quasi-Newton and nonlinear conjugate gradient implementation adapted to the manifold with a projected nonlinear conjugate gradient method, and demonstrate that the convergence rate is significantly improved if the manifold is taken into account when designing the optimization procedure.
ISSN:2331-8422