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Integer Quadratic Quasi-polyhedra

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Integer Programming and Combinatorial Optimization (IPCO 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6080))

Abstract

This paper introduces two fundamental families of ‘quasi-polyhedra’ — polyhedra with a countably infinite number of facets — that arise in the context of integer quadratic programming. It is shown that any integer quadratic program can be reduced to the minimisation of a linear function over a quasi-polyhedron in the first family. Some fundamental properties of the quasi-polyhedra are derived, along with connections to some other well-studied convex sets. Several classes of facet-inducing inequalities are also derived. Finally, extensions to the mixed-integer case are briefly examined.

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Author information

Authors and Affiliations

  1. Department of Management Science, Lancaster University, Lancaster, LA1 4YW, United Kingdom

    Adam N. Letchford

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  1. Adam N. Letchford
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Editors and Affiliations

  1. Institute of Mathematics, École Polytechnique Féderale de Lausanne, 1015, Lausanne, Switzerland

    Friedrich Eisenbrand

  2. McGill University, 805 Sherbrooke West, H3A 2K6, Montreal, Quebec, Canada

    F. Bruce Shepherd

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Letchford, A.N. (2010). Integer Quadratic Quasi-polyhedra. In: Eisenbrand, F., Shepherd, F.B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2010. Lecture Notes in Computer Science, vol 6080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13036-6_20

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  • DOI: https://doi.org/10.1007/978-3-642-13036-6_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13035-9

  • Online ISBN: 978-3-642-13036-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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