A polyhedral characterization of the inverse-feasible region of a mixed-integer program

Given a feasible solution x0x0 to a mixed-integer program (MIP), the inverse MIP problem is to find an objective dd such that x0x0 is optimal for the MIP with objective function dd, and among all such objectives, the distance from a given target objective is minimized. By using a novel expression for the MIP value function, we formulate the inverse MIP problem as a linear program (LP), albeit of exponentially large size.