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On branching-point selection for trilinear monomials in spatial branch-and-bound: the hull relaxation

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  • Emily Speakman

    (University of Michigan)

  • Jon Lee

    (University of Michigan)

Abstract

In Speakman and Lee (Math Oper Res 42(4):1230–1253, 2017), we analytically developed the idea of using volume as a measure for comparing relaxations in the context of spatial branch-and-bound. Specifically, for trilinear monomials, we analytically compared the three possible “double-McCormick relaxations” with the tight convex-hull relaxation. Here, again using volume as a measure, for the convex-hull relaxation of trilinear monomials, we establish simple rules for determining the optimal branching variable and optimal branching point. Additionally, we compare our results with current software practice.

Suggested Citation

  • Emily Speakman & Jon Lee, 2018. "On branching-point selection for trilinear monomials in spatial branch-and-bound: the hull relaxation," Journal of Global Optimization, Springer, vol. 72(2), pages 129-153, October.
    • Handle: RePEc:spr:jglopt:v:72:y:2018:i:2:d:10.1007_s10898-018-0620-7
    DOI: 10.1007/s10898-018-0620-7
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    References listed on IDEAS

    as
    1. Emily Speakman & Jon Lee, 2017. "Quantifying Double McCormick," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1230-1253, November.
    2. Ruth Misener & Christodoulos Floudas, 2013. "GloMIQO: Global mixed-integer quadratic optimizer," Journal of Global Optimization, Springer, vol. 57(1), pages 3-50, September.
    3. Sonia Cafieri & Jon Lee & Leo Liberti, 2010. "On convex relaxations of quadrilinear terms," Journal of Global Optimization, Springer, vol. 47(4), pages 661-685, August.
    4. Ruth Misener & Christodoulos Floudas, 2014. "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations," Journal of Global Optimization, Springer, vol. 59(2), pages 503-526, July.
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    Cited by:

    1. Kurt M. Anstreicher & Samuel Burer & Kyungchan Park, 2021. "Convex hull representations for bounded products of variables," Journal of Global Optimization, Springer, vol. 80(4), pages 757-778, August.
    2. Jon Lee & Daphne Skipper & Emily Speakman, 2022. "Gaining or losing perspective," Journal of Global Optimization, Springer, vol. 82(4), pages 835-862, April.
    3. Wei Jiang & Huiqiang Wang & Bingyang Li & Haibin Lv & Qingchuan Meng, 2020. "A multi-user multi-operator computing pricing method for Internet of things based on bi-level optimization," International Journal of Distributed Sensor Networks, , vol. 16(1), pages 15501477199, January.

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