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

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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.

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Acknowledgments

The author is very grateful to two anonymous reviewers, whose comments helped a lot to improve the original version of the paper.

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  1. Dipartimento di Ingegneria dell’Informazione, Università di Parma, Via G.P. Usberti, 181/A, 43124 , Parma, Italy

    Marco Locatelli

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  1. Marco Locatelli
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Correspondence to Marco Locatelli.

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Locatelli, M. A technique to derive the analytical form of convex envelopes for some bivariate functions. J Glob Optim 59, 477–501 (2014). https://doi.org/10.1007/s10898-014-0177-z

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  • DOI: https://doi.org/10.1007/s10898-014-0177-z

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