Two algorithms for the lower bound method of reduced density matrix theory

We analyze the lower bound method of reduced density matrix theory, a method which obtains a lower bound to the ground state energy of a many-fermion system as well as an approximation to the corresponding reduced density matrix. Our main result is a theorem giving necessary and sufficient conditions for the optimum for the central optimization problem of this method. Based on this theorem we have developed two algorithms for solving this optimization problem. We consider their convergence properties.