  A pointed convex cone naturally induces a partial order, and further a notion
of nondecreasingness for functions. We consider extended real-valued functions
defined on the cone. Monotone conjugates for these functions can be defined in
an analogous way to the standard convex conjugate. The only difference is that
the supremum is taken over the cone instead of the entire space. We give
sufficient conditions for the cone under which the corresponding Fenchel-Moreau
biconjugation identity holds for proper, convex, lower semicontinuous, and
nondecreasing functions defined on the cone. In addition, we show that these
conditions are satisfied by a class of cones known as perfect cones.
