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Convex envelope of bivariate cubic functions over rectangular regions

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  • Marco Locatelli

    (Università di Parma)

Abstract

In recent years many papers have derived polyhedral and non-polyhedral convex envelopes for different classes of functions. Except for the univariate cases, all these classes of functions share the property that the generating set of their convex envelope is a subset of the border of the region over which the envelope is computed. In this paper we derive the convex envelope over a rectangular region for a class of functions which does not have this property, namely the class of bivariate cubic functions without univariate third-degree terms.

Suggested Citation

  • Marco Locatelli, 2020. "Convex envelope of bivariate cubic functions over rectangular regions," Journal of Global Optimization, Springer, vol. 76(1), pages 1-24, January.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:1:d:10.1007_s10898-019-00846-2
    DOI: 10.1007/s10898-019-00846-2
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    References listed on IDEAS

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    1. Marco Locatelli, 2018. "Convex envelopes of bivariate functions through the solution of KKT systems," Journal of Global Optimization, Springer, vol. 72(2), pages 277-303, October.
    2. Martin Ballerstein & Dennis Michaels, 2014. "Extended formulations for convex envelopes," Journal of Global Optimization, Springer, vol. 60(2), pages 217-238, October.
    3. Rida Laraki & Jean-Bernard Lasserre, 2008. "Computing uniform convex approximations for convex envelopes and convex hulls," Post-Print hal-00243009, HAL.
    4. Marco Locatelli, 2016. "Non polyhedral convex envelopes for 1-convex functions," Journal of Global Optimization, Springer, vol. 65(4), pages 637-655, August.
    5. Joseph Scott & Matthew Stuber & Paul Barton, 2011. "Generalized McCormick relaxations," Journal of Global Optimization, Springer, vol. 51(4), pages 569-606, December.
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    Cited by:

    1. M. Locatelli, 2022. "Exact and approximate results for convex envelopes of special structured functions over simplices," Journal of Global Optimization, Springer, vol. 83(2), pages 201-220, June.

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