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.
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The author is extremely grateful to an anonymous reviewer for his/her careful reading and for the very detailed comments, which considerably helped to improve the paper with respect to its original version.
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Locatelli, M. Convex envelope of bivariate cubic functions over rectangular regions. J Glob Optim 76, 1–24 (2020). https://doi.org/10.1007/s10898-019-00846-2
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DOI: https://doi.org/10.1007/s10898-019-00846-2