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Simple Odd \(\beta \)-Cycle Inequalities for Binary Polynomial Optimization

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Integer Programming and Combinatorial Optimization (IPCO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13265))

Abstract

We consider the multilinear polytope which arises naturally in binary polynomial optimization. Del Pia and Di Gregorio introduced the class of odd \(\beta \)-cycle inequalities valid for this polytope, showed that these generally have Chvátal 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 \(\beta \)-cycle inequalities, for which we establish a strongly polynomial-time separation algorithm for arbitrary instances. These inequalities still have Chvátal rank 2 in general and still suffice to describe the multilinear polytope for cycle hypergraphs.

A. Del Pia is partially funded by ONR grant N00014-19-1-2322. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the Office of Naval Research. M. Walter acknowledges funding support from the Dutch Research Council (NWO) on grant number OCENW.M20.151.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, USA

    Alberto Del Pia

  2. Department of Applied Mathematics, University of Twente, Enschede, The Netherlands

    Matthias Walter

Authors
  1. Alberto Del Pia
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  2. Matthias Walter
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Correspondence to Matthias Walter .

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Editors and Affiliations

  1. Delft University of Technology, Delft, The Netherlands

    Karen Aardal

  2. Eindhoven University of Technology, Eindhoven, The Netherlands

    Laura Sanità

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Del Pia, A., Walter, M. (2022). Simple Odd \(\beta \)-Cycle Inequalities for Binary Polynomial Optimization. In: Aardal, K., Sanità, L. (eds) Integer Programming and Combinatorial Optimization. IPCO 2022. Lecture Notes in Computer Science, vol 13265. Springer, Cham. https://doi.org/10.1007/978-3-031-06901-7_14

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  • DOI: https://doi.org/10.1007/978-3-031-06901-7_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-06900-0

  • Online ISBN: 978-3-031-06901-7

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