# IPO

IPO - Investigating Polyhedra by Oracles. The software framework IPO (Investigating Polyhedra by Oracles) is presented which allows to analyze polyhedra that are given only implicitly by an optimization oracle. The motivation comes from polyhedral combinatorics, where the oracle can easily be provided by a mixed-integer-programming solver. IPO detects a full system of equations and some facets of the implicitly given polyhedron with exact arithmetic. The facets are produced in such a way that they are helpful in optimizing a given objective function. This is in contrast to usual convex-hull algorithms which produce the entire description of a polyhedron, but run out of resources for small dimensions already. Thus, IPO can typically handle larger dimensions. In the talk we will briefly discuss how IPO actually works, followed by a demonstration of its capabilities. For this we consider short computational studies, namely dimension analysis of MIPLIB 2.0, facet-detection for matching polytopes with one quadratic objective term and adjacency statistics for TSP polytopes. IPO is available at http://polyhedra-oracles.bitbucket.org/.