CONVERGENT ITERATIVE METHODS FOR THE HARTREE EIGENPROBLEM

This paper develops some new variational principles for the solutions of Hartree eigenproblems and uses these characterizations to describe convergent iterative algorithms for these problems. This is done first for-helium and then for general atoms and molecules. The variational principles involve minimizing separately convex functionals over the p roduct of convex sets. By minimizing in different variables at each st ep, we are led to descent methods where at each step there is a strict ly convex problem with a unique solution. The resulting sequence is sh own to converge to a solution of the Hartree eigenproblem.