Erratum to: MIR closures of polyhedral sets

In Section 3.3 of the paper [3], we compare our nonlinear separation model (MIR-SEP) for MIR cuts with the one for split cuts (PMILP) presented in Balas and Saxena [1] and show that (Lemma 9) they are equivalent. We then present a numerical example to show that the linearized separation models are not equivalent and make the following claim without a proof: “The Balas/Saxena model PMILP for this example (or more precisely, the deparametrized model MILP(θ )) is infeasible unless the parameter θ is chosen to be exactly 0.31.” This claim is incorrect (as pointed out to us by Balas and Saxena) and contains two errors. The first is that Balas and Saxena [1] assume that all variables are non-negative, whereas the example in our paper contains a free variable. Secondly, for any problem in the correct format (including the one obtained by replacing the free variable in our example by two non-negative variables) MILP(θ ) is feasible for all θ ∈ (0, 1).