When the Gomory–Chvátal closure coincides with the integer hull

Abstract

Gomory–Chvátal cuts are prominent in integer programming. The Gomory–Chvátal closure of a polyhedron is the intersection of the half spaces defined by all its Gomory–Chvátal cuts. We prove that it is NP-hard to decide whether the Gomory–Chvátal closure of a rational polyhedron P is identical to the integer hull of P. An earlier version of this paper appeared in the proceedings of IPCO 2016.