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On convergence in mixed integer programming
Let be a rational polyhedron, and let P I be the convex hull of . We define the integral lattice-free closure of P as the set obtained from P by adding all inequalities obtained from disjunctions associated with integral lattice-free polyhedra in . We show that the integral lattice-free closure of P is again a polyhedron, and that repeatedly taking the integral lattice-free closure of P gives P I after a finite number of iterations. Such results can be seen as a mixed integer analogue of theorems by Chvátal and Schrijver for the pure integer case. One ingredient of our proof is an extension of a result by Owen and Mehrotra. In fact, we prove that for each rational polyhedron P, the split closures of P yield in the limit the set P
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