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We consider the problem of minimising functions represented as a differenceof lattice submodular functions. We propose analogues to the SupSub, SubSup andModMod routines for lattice submodular functions. We show that ourmajorisation-minimisation algorithms produce iterates that monotonicallydecrease, and that we converge to a local minimum. We also extend additivehardness results, and show that a broad range of functions can be expressed asthe difference of submodular functions.

Majorisation-minimisation algorithms for minimising the difference between lattice submodular functions