ABSTRACT
A well known result on unions of polyhedra in the same space gives an extended formulation whose projection is the convex hull of the union. Here we examine the union of monotone polytopes in disjoint spaces, and for this case we give a complete description of the convex hull without additional variables, along with a linear time separation algorithm. These results are based on an explicit representation of the dominant of a polytope. Special cases include logical conditions of varying complexity (generalizing a result of Hong and Hooker), knapsack configurations (generalizing a result of Padberg), matroid polyhedra and polymatroids (generalizing results of Conforti and Laurent). This talk is based on joint work with Alexander Bockmayr, Nicolai Pisaruk and Laurence Wolsey.