  In this review, we will discuss the results of our recent work to study the
general optimization of the pure isovector parameters of the popular
relativistic mean-field (RMF) and Skyrme-Hartree-Fock (SHF) nuclear
energy-density functionals (EDFs), using constraints on the pure neutron matter
(PNM) equation of state (EoS) from recent {\sl ab initio} calculations. By
using RMF and SHF parameterizations that give equivalent predictions for
ground-state properties of doubly magic nuclei and properties of symmetric
nuclear matter (SNM) and PNM, we found that such optimization leads to broadly
consistent symmetry energy $J$ and its slope parameter $L$ at saturation
density within a tight range of $\sigma(J) < 2$ MeV and $\sigma(L) < 6$ MeV. We
demonstrate that a clear model dependence shows up (a) in the curvature
parameter of the symmetry energy $K_{\rm sym}$, (b) the symmetry energy at
supra-saturation densities, and (c) the radius of neutron stars.
