Characterization of the split closure via geometric lifting

Amitabh Basu and Marco Molinaro

European Journal of Operational Research, 2015, vol. 243, issue 3, 745-751

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).

Keywords: Integer programming; Cutting-plane; Split cut; Cut-generating function; Geometric lifting (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:243:y:2015:i:3:p:745-751

DOI: 10.1016/j.ejor.2014.12.018

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