Density matrix minimization with ${\ell }_1$ regularization

Abstract

We propose a convex variational principle to find sparse representation of low-lying eigenspace of symmetric matrices. In the context of electronic structure calculation, this corresponds to a sparse density matrix minimization algorithm with ${\ell }_1$ regularization. The minimization problem can be efficiently solved by a split Bergman iteration type algorithm. We further prove that from any initial condition, the algorithm converges to a minimizer of the variational principle.

25 pages, 11 figures

References in corpus (1)

• Compressed Modes for Variational Problems in Mathematics and Physics