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Cardinality Constrained Multilinear Sets

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Combinatorial Optimization (ISCO 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12176))

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Abstract

The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set, and many valid inequalities for its convex hull are available in the literature. Motivated by a machine learning application, we study a cardinality constrained version of this problem with upper and lower bounds on the number of nonzero variables. We call the set of solutions of the standard linearization of this problem a cardinality constrained multilinear set, and give a complete polyhedral description of its convex hull when the multilinear terms in the problem have a nested structure.

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Author information

Authors and Affiliations

  1. University of Wisconsin-Madison, Madison, WI, 53706, USA

    Rui Chen

  2. IBM T. J. Watson Research Center, Yorktown Heights, NY, 10598, USA

    Sanjeeb Dash

  3. School of ORIE, Cornell University, Ithaca, NY, 14853, USA

    Oktay Günlük

Authors
  1. Rui Chen
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  2. Sanjeeb Dash
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  3. Oktay Günlük
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Corresponding author

Correspondence to Rui Chen .

Editor information

Editors and Affiliations

  1. CNRS and Université Clermont Auvergne, Aubière, France

    Mourad Baïou

  2. Département d'informatique et de recherche opérationnelle & CIRRELT, University of Montreal, Montréal, QC, Canada

    Bernard Gendron

  3. School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA

    Oktay Günlük

  4. Laboratoire LAMSADE, Université Paris-Dauphine, Paris, France

    A. Ridha Mahjoub

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Chen, R., Dash, S., Günlük, O. (2020). Cardinality Constrained Multilinear Sets. In: Baïou, M., Gendron, B., Günlük, O., Mahjoub, A.R. (eds) Combinatorial Optimization. ISCO 2020. Lecture Notes in Computer Science(), vol 12176. Springer, Cham. https://doi.org/10.1007/978-3-030-53262-8_5

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  • DOI: https://doi.org/10.1007/978-3-030-53262-8_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-53261-1

  • Online ISBN: 978-3-030-53262-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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