  We survey approaches to nonrelativistic density functional theory (DFT) for
nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab
initio DFT starts with a microscopic Hamiltonian and is naturally formulated
using orbital-based functionals, which generalize the conventional
local-density-plus-gradients form. The orbitals satisfy single-particle
equations with multiplicative (local) potentials. The DFT functionals can be
developed starting from internucleon forces using wave-function based methods
or by Legendre transform via effective actions. We describe known and
unresolved issues for applying these formulations to the nuclear many-body
problem and discuss how ab initio approaches can help improve empirical energy
density functionals.
