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Compact linearization for binary quadratic problems subject to assignment constraints

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  • Sven Mallach

    (Universität zu Köln)

Abstract

We introduce and prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints that has been proposed by Liberti (4OR 5(3):231–245, 2007, https://doi.org/10.1007/s10288-006-0015-3 ). The new conditions resolve inconsistencies that can occur when the original method is used. We also present a mixed-integer linear program to compute a minimally sized linearization. When all the assignment constraints have non-overlapping variable support, this program is shown to have a totally unimodular constraint matrix. Finally, we give a polynomial-time combinatorial algorithm that is exact in this case and can be used as a heuristic otherwise.

Suggested Citation

  • Sven Mallach, 2018. "Compact linearization for binary quadratic problems subject to assignment constraints," 4OR, Springer, vol. 16(3), pages 295-309, September.
    • Handle: RePEc:spr:aqjoor:v:16:y:2018:i:3:d:10.1007_s10288-017-0364-0
    DOI: 10.1007/s10288-017-0364-0
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    References listed on IDEAS

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    5. Warren P. Adams & Hanif D. Sherali, 1986. "A Tight Linearization and an Algorithm for Zero-One Quadratic Programming Problems," Management Science, INFORMS, vol. 32(10), pages 1274-1290, October.
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    Cited by:

    1. Sven Mallach, 2021. "Inductive linearization for binary quadratic programs with linear constraints," 4OR, Springer, vol. 19(4), pages 549-570, December.

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