) and likewise for (T s ) γ . Importantly, F γ and (T s ) γ are both everywhere differentiable, meaning that the interacting and noninteracting Euler-Lagrange equations can now be solved simultaneously. In convex analysis, such a procedure is known as the Moreau-Yosida regularization. Once the regularized energy E γ [v] has been calculated, it is trivial to obtain E[v] and nothing is lost -that is, the Moreau-Yosida regularization of F has the curious property of being lossless with respect to the calculation of the ground-state energy E[v]. The only caveat is that v must be finite, which is only satisfied for Coulomb potentials by constraining the system to an arbitrarily large box.