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Non polyhedral convex envelopes for 1-convex functions

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  • Marco Locatelli

    (Università di Parma)

Abstract

In this paper we discuss how to derive the non polyhedral convex envelopes for some functions, called 1-convex throughout the paper, over boxes. The main result is about n-dimensional 1-convex functions, but we get to it by first discussing in detail some special cases, namely functions $$xyz^\delta $$ x y z δ , $$\delta >1$$ δ > 1 , and, next, more general trivariate functions. The relation between the class of functions investigated in this paper and other classes investigated in the existing literature is discussed.

Suggested Citation

  • Marco Locatelli, 2016. "Non polyhedral convex envelopes for 1-convex functions," Journal of Global Optimization, Springer, vol. 65(4), pages 637-655, August.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:4:d:10.1007_s10898-016-0409-5
    DOI: 10.1007/s10898-016-0409-5
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    References listed on IDEAS

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    1. 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.
    2. 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, 2020. "Convex envelope of bivariate cubic functions over rectangular regions," Journal of Global Optimization, Springer, vol. 76(1), pages 1-24, January.
    2. 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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