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The exact reduced density-matrix functional is derived from theLuttinger-Ward functional of the single-particle Green's function. Thereby, aformal link is provided between diagrammatic many-body approaches using Green'sfunctions on the one hand and theories based on many-body wave functions on theother. This link can be used to explicitly construct approximations for thedensity-matrix functional that are equivalent to standard diagrammaticre-summation techniques and to non-perturbative dynamical mean-field theory inparticular. Contrary to functionals of the Green's-function, the exactdensity-matrix functional is convex and thus provides a true minimum principlewhich facilitates the calculation of the grand potential and derivedequilibrium properties. The benefits of the proposed Green's-function-baseddensity-matrix functional theory for geometrical structure optimization ofstrongly correlated materials are discussed.

Density-matrix functionals from Greens functions