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.

Convex envelope of bivariate cubic functions over rectangular regions / Locatelli, M.. - In: JOURNAL OF GLOBAL OPTIMIZATION. - ISSN 0925-5001. - 76:(2020), pp. 1-24. [10.1007/s10898-019-00846-2]

Convex envelope of bivariate cubic functions over rectangular regions

Locatelli M.
2020-01-01

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.
2020
Convex envelope of bivariate cubic functions over rectangular regions / Locatelli, M.. - In: JOURNAL OF GLOBAL OPTIMIZATION. - ISSN 0925-5001. - 76:(2020), pp. 1-24. [10.1007/s10898-019-00846-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2866318
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