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A technique to derive the analytical form of convex envelopes for some bivariate functions

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  • Marco Locatelli

Abstract

In the recent paper (Locatelli and Schoen in Math Program, 2013 ) it is shown that the value of the convex envelope of some bivariate functions over polytopes can be computed by solving a continuously differentiable convex problem. In this paper we show how this result can be exploited to derive in some cases the analytical form of the envelope. The technique is illustrated through two examples. Copyright Springer Science+Business Media New York 2014

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  • Marco Locatelli, 2014. "A technique to derive the analytical form of convex envelopes for some bivariate functions," Journal of Global Optimization, Springer, vol. 59(2), pages 477-501, July.
    • Handle: RePEc:spr:jglopt:v:59:y:2014:i:2:p:477-501
    DOI: 10.1007/s10898-014-0177-z
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    References listed on IDEAS

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    1. Faiz A. Al-Khayyal & James E. Falk, 1983. "Jointly Constrained Biconvex Programming," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 273-286, May.
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    Cited by:

    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. Marco Locatelli, 2016. "Polyhedral subdivisions and functional forms for the convex envelopes of bilinear, fractional and other bivariate functions over general polytopes," Journal of Global Optimization, Springer, vol. 66(4), pages 629-668, December.
    3. Marco Locatelli, 2016. "Non polyhedral convex envelopes for 1-convex functions," Journal of Global Optimization, Springer, vol. 65(4), pages 637-655, August.
    4. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.

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