Density matrix minimization with $\ell_1$ regularization
  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. 
Rongjie Lai, Jianfeng Lu, Stanley Osher
math-ph math.MP math.NA physics.comp-ph