Why not both? Exact continuous and discrete optimization with submodularity

Jonathan Bunton, Paulo Tabuada

Abstract: Submodularity is a pivotal property of functions defined on lattices, as it permits their exact minimization and approximate maximization in polynomial time. In this work, we examine submodular function minimization defined on continuous and discrete lattices simultaneously. We identify a class of these mixed optimization problems that can be exactly solved by applying a combination of submodular and convex optimization routines. The utility of this approach is demonstrated via several examples from the proposed class of optimization problems.