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On the exhaustivity of simplicial partitioning

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  • Peter Dickinson

Abstract

During the last 40 years, simplicial partitioning has been shown to be highly useful, including in the field of nonlinear optimization, specifically global optimization. In this article, we consider results on the exhaustivity of simplicial partitioning schemes. We consider conjectures on this exhaustivity which seem at first glance to be true (two of which have been stated as true in published articles). However, we will provide counter-examples to these conjectures. We also provide a new simplicial partitioning scheme, which provides a lot of freedom, whilst guaranteeing exhaustivity. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Peter Dickinson, 2014. "On the exhaustivity of simplicial partitioning," Journal of Global Optimization, Springer, vol. 58(1), pages 189-203, January.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:1:p:189-203
    DOI: 10.1007/s10898-013-0040-7
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    References listed on IDEAS

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    1. Hendrix, Eligius M.T. & Casado, Leocadio G. & Garcí­a, Inmaculada, 2008. "The semi-continuous quadratic mixture design problem: Description and branch-and-bound approach," European Journal of Operational Research, Elsevier, vol. 191(3), pages 803-815, December.
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    Cited by:

    1. Akihiro Tanaka & Akiko Yoshise, 2018. "LP-based tractable subcones of the semidefinite plus nonnegative cone," Annals of Operations Research, Springer, vol. 265(1), pages 155-182, June.
    2. Mohammadreza Safi & Seyed Saeed Nabavi & Richard J. Caron, 2021. "A modified simplex partition algorithm to test copositivity," Journal of Global Optimization, Springer, vol. 81(3), pages 645-658, November.
    3. Peiping Shen & Dianxiao Wu & Kaimin Wang, 2023. "Globally minimizing a class of linear multiplicative forms via simplicial branch-and-bound," Journal of Global Optimization, Springer, vol. 86(2), pages 303-321, June.

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