Inverse of the Gomory corner relaxation of integer programs

We explore the inverse of integer programs (IPs) by studying the inverse of their Gomory corner relaxations (GCRs). We propose a linear programming (LP) formulation for solving any inverse GCR problem under the L 1 and L ∞ norms by reformulating the inverse GCR problem as the inverse of a shortest path problem. We show that the minimum objective of the inverse GCR across all feasible bases of the LP relaxation yields an upper bound on the optimal value of the inverse IP that is at least as tight as the optimal value of the inverse of the LP relaxation. We provide conditions under which this upper bound is exactly equal to the optimal value of the inverse IP.