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The Running Intersection Relaxation of the Multilinear Polytope

Author

Listed:
  • Alberto Del Pia

    (Department of Industrial and systems Engineering and Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, Wisconsin 53706)

  • Aida Khajavirad

    (Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, Pennsylvania 18015)

Abstract

The multilinear polytope of a hypergraph is the convex hull of a set of binary points satisfying a collection of multilinear equations. We introduce the running intersection inequalities, a new class of facet-defining inequalities for the multilinear polytope. Accordingly, we define a new polyhedral relaxation of the multilinear polytope, referred to as the running intersection relaxation, and identify conditions under which this relaxation is tight. Namely, we show that for kite-free beta-acyclic hypergraphs, a class that lies between gamma-acyclic and beta-acyclic hypergraphs, the running intersection relaxation coincides with the multilinear polytope and it admits a polynomial size extended formulation.

Suggested Citation

  • Alberto Del Pia & Aida Khajavirad, 2021. "The Running Intersection Relaxation of the Multilinear Polytope," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 1008-1037, August.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:3:p:1008-1037
    DOI: 10.1287/moor.2021.1121
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