Simple odd β-cycle inequalities for binary polynomial optimization

Alberto Del Pia, Matthias Walter

Research output: Working paperProfessional

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Abstract

We consider the multilinear polytope which arises naturally in binary polynomial optimization. Del Pia and Di Gregorio introduced the class of odd β-cycle inequalities valid for this polytope, showed that these generally have Chv{á}tal rank 2 with respect to the standard relaxation and that, together with flower inequalities, they yield a perfect formulation for cycle hypergraph instances. Moreover, they describe a separation algorithm in case the instance is a cycle hypergraph. We introduce a weaker version, called simple odd β-cycle inequalities, for which we establish a strongly polynomial-time separation algorithm for arbitrary instances. These inequalities still have Chv{á}tal rank 2 in general and still suffice to describe the multilinear polytope for cycle hypergraphs. Finally, we report about computational results of our prototype implementation. The simple odd β-cycle inequalities sometimes help to close more of the integrality gap in the experiments; however, the preliminary implementation has substantial computational cost, suggesting room for improvement in the separation algorithm.
Original languageEnglish
PublisherArXiv.org
Number of pages21
DOIs
Publication statusPublished - 8 Nov 2021

Keywords

  • cs.DM
  • math.CO
  • 90C57
  • G.2.0

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