In this paper we exploit a slight variant of a result previously proved in Locatelli and Schoen (Math Program 144:65–91, 2014) to define a procedure which delivers the convex envelope of some bivariate functions over polytopes. The procedure is based on the solution of a KKT system and simplifies the derivation of the convex envelope with respect to previously proposed techniques. The procedure is applied to derive the convex envelope of the bilinear function xy over any polytope, and the convex envelope of functions xnym over boxes.

Convex envelopes of bivariate functions through the solution of KKT systems / Locatelli, Marco. - In: JOURNAL OF GLOBAL OPTIMIZATION. - ISSN 0925-5001. - 72:2(2018), pp. 277-303. [10.1007/s10898-018-0626-1]

Convex envelopes of bivariate functions through the solution of KKT systems

Locatelli, Marco
2018

Abstract

In this paper we exploit a slight variant of a result previously proved in Locatelli and Schoen (Math Program 144:65–91, 2014) to define a procedure which delivers the convex envelope of some bivariate functions over polytopes. The procedure is based on the solution of a KKT system and simplifies the derivation of the convex envelope with respect to previously proposed techniques. The procedure is applied to derive the convex envelope of the bilinear function xy over any polytope, and the convex envelope of functions xnym over boxes.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2856288
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