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Characterization of the split closure via geometric lifting

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  • Basu, Amitabh
  • Molinaro, Marco

Abstract

We analyze split cuts from the perspective of cut generating functions via geometric lifting. We show that α-cuts, a natural higher-dimensional generalization of the k-cuts of Cornuéjols et al., give all the split cuts for the mixed-integer corner relaxation. As an immediate consequence we obtain that the k-cuts are equivalent to split cuts for the 1-row mixed-integer relaxation. Further, we show that split cuts for finite-dimensional corner relaxations are restrictions of split cuts for the infinite-dimensional relaxation. In a final application of this equivalence, we exhibit a family of pure-integer programs whose split closure has arbitrarily bad integrality gap. This complements the mixed-integer example provided by Basu et al. (2011).

Suggested Citation

  • Basu, Amitabh & Molinaro, Marco, 2015. "Characterization of the split closure via geometric lifting," European Journal of Operational Research, Elsevier, vol. 243(3), pages 745-751.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:3:p:745-751
    DOI: 10.1016/j.ejor.2014.12.018
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    References listed on IDEAS

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    1. Kent Andersen & Gérard Cornuéjols & Yanjun Li, 2005. "Reduce-and-Split Cuts: Improving the Performance of Mixed-Integer Gomory Cuts," Management Science, INFORMS, vol. 51(11), pages 1720-1732, November.
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