  The exact reduced density-matrix functional is derived from the
Luttinger-Ward functional of the single-particle Green's function. Thereby, a
formal link is provided between diagrammatic many-body approaches using Green's
functions on the one hand and theories based on many-body wave functions on the
other. This link can be used to explicitly construct approximations for the
density-matrix functional that are equivalent to standard diagrammatic
re-summation techniques and to non-perturbative dynamical mean-field theory in
particular. Contrary to functionals of the Green's-function, the exact
density-matrix functional is convex and thus provides a true minimum principle
which facilitates the calculation of the grand potential and derived
equilibrium properties. The benefits of the proposed Green's-function-based
density-matrix functional theory for geometrical structure optimization of
strongly correlated materials are discussed.
