  A conceptual difficulty in formulating the density functional theory of the
fractional quantum Hall effect is that while in the standard approach the
Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the
fractional quantum Hall effect calls for fractionally occupied Kohn-Sham
orbitals. This has necessitated averaging over an ensemble of Slater
determinants to obtain meaningful results. We develop an alternative approach
in which we express and minimize the grand canonical potential in terms of the
composite fermion variables. This provides a natural resolution of the
fractional-occupation problem because the fully occupied orbitals of composite
fermions automatically correspond to fractionally occupied orbitals of
electrons. We demonstrate the quantitative validity of our approach by
evaluating the density profile of fractional Hall edge as a function of
temperature and the distance from the delta dopant layer and showing that it
reproduces edge reconstruction in the expected parameter region.
