Minimizing a Submodular Function on a Lattice - Topkis, Donald M. (Operations Research, 1978)
This paper gives general conditions under which a collection of optimization problems, with the objective function and the constraint set depending on a parameter, has optimal solutions that are an isotone function of the parameter. Relating to this, we present a theory that explores and elaborates on the problem of minimizing a submodular function on a lattice.