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Nonlinear Assignment Problems pp 143–174Cite as

Semidefinite Programming Approaches to the Quadratic Assignment Problem

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Part of the book series: Combinatorial Optimization ((COOP,volume 7))

Abstract

The Quadratic Assignment Problem, QAP, is arguably the hardest of the NP-hard problems. One of the main reasons is that it is very difficult to get good quality bounds for branch and bound algorithms. We show that many of the bounds that have appeared in the literature can be ranked and put into a unified Semidefinite Programming, SDP, framework. This is done using redundant quadratic constraints and Lagrangian relaxation. Thus, the final SDP relaxation ends up being the strongest.

Research partially supported by The Natural Sciences Engineering Research Council Canada.

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Author information

Authors and Affiliations

  1. Department of Combinatorics and Optimization , Waterloo, Ontario, N2L 3G1, Canada

    Henry Wolkowicz

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  1. Henry Wolkowicz
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Editors and Affiliations

  1. University of Florida, USA

    Panos M. Pardalos

  2. Princeton University, USA

    Leonidas S. Pitsoulis

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Wolkowicz, H. (2000). Semidefinite Programming Approaches to the Quadratic Assignment Problem. In: Pardalos, P.M., Pitsoulis, L.S. (eds) Nonlinear Assignment Problems. Combinatorial Optimization, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3155-2_7

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  • DOI: https://doi.org/10.1007/978-1-4757-3155-2_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4841-0

  • Online ISBN: 978-1-4757-3155-2

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