Abstract
A cutting-plane procedure for integer programming (IP) problems usually involves invoking a black-box procedure (such as the Gomory-Chvátal (GC) procedure) to compute a cutting-plane. In this paper, we describe an alternative paradigm of using the same cutting-plane black-box. This involves two steps. In the first step, we design an inequality cx ≤ d, independent of the cutting-plane black-box. In the second step, we verify that the designed inequality is a valid inequality by verifying that the set P ∩ {x ∈ ℝn: cx ≥ d + 1} ∩ ℤn is empty using cutting-planes from the black-box. Here P is the feasible region of the linear-programming relaxation of the IP. We refer to the closure of all cutting-planes that can be verified to be valid using a specific cutting-plane black-box as the verification closure of the considered cutting-plane black-box. This paper conducts a systematic study of properties of verification closures of various cutting-plane black-box procedures.
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Dey, S.S., Pokutta, S. (2011). Design and Verify: A New Scheme for Generating Cutting-Planes. In: Günlük, O., Woeginger, G.J. (eds) Integer Programming and Combinatoral Optimization. IPCO 2011. Lecture Notes in Computer Science, vol 6655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20807-2_12
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DOI: https://doi.org/10.1007/978-3-642-20807-2_12
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