  For a quantum-mechanical many-electron system, given a density, the
Zhao-Morrison-Parr method allows to compute the effective potential that yields
precisely that density. In this work, we demonstrate how this and similar
inversion procedures mathematically relate to the Moreau-Yosida regularization
of density functionals on Banach spaces. It is shown that these inversion
procedures can in fact be understood as a limit process as the regularization
parameter approaches zero. This sheds new insight on the role of Moreau-Yosida
regularization in density-functional theory and allows to systematically
improve density-potential inversion. Our results apply to the Kohn-Sham setting
with fractional occupation that determines an effective one-body potential that
in turn reproduces an interacting density.
