  We consider the problem of minimising functions represented as a difference
of lattice submodular functions. We propose analogues to the SupSub, SubSup and
ModMod routines for lattice submodular functions. We show that our
majorisation-minimisation algorithms produce iterates that monotonically
decrease, and that we converge to a local minimum. We also extend additive
hardness results, and show that a broad range of functions can be expressed as
the difference of submodular functions.
