The calculations of electronic ground state energies, following either the Hartree-Fock or the Kohn-Sham schemes, are major issues in quantum chemistry. In a recent publication, we have proposed a new numerical method, namely the relaxed constrained algorithms (RCA), to solve the Hartree-Fock problem. The purpose of the present paper is to discuss the extension of this method to the case of the Kohn-Sham problem. It is shown that RCA seems to be more robust than other self-consistent field algorithms currently used and that they provide in addition a natural way to solve the extended Kohn-Sham problem, obtained by allowing fractional occupancy of the single-particle orbitals.