## Computation on polymatroidal functions

Consider a set function $f$ defined over a ground set $S,$ $f:2^S\to \mathbb{R}$ that satisfies the polymatroidal axioms. I am provided certain constraints on the value of the function for some subsets. I want to obtain a bound on the value of the function for the whole set $S.$ I would be glad to know some literature on algorithms for this kind of computation. If there is any software package that can perform these computations, that would be useful too.

Thanks.

-