Density matrix minimization with ${\ell}_1$ regularization
Rongjie Lai, Jianfeng Lu, Stanley Osher · Communications in Mathematical Sciences · 2015
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 ℓ 1 regularization.The minimization problem can be efficiently solved by a split Bregman iteration type algorithm.We further prove that from any initial condition, the algorithm converges to a minimizer of the variational principle.