Convex envelope of bivariate cubic functions over rectangular regions
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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.
KeywordsConvex envelope Generating set Cubic functions
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.
- 16.Tardella, F.: On the existence of polyhedral convex envelopes. In: Floudas, C.A., Pardalos, P.M. (eds.) Frontiers in Global Optimization, pp. 563–574. Kluwer, Dordrecht (2003)Google Scholar