Convex envelopes of bivariate functions through the solution of KKT systems

Marco Locatelli ()
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Marco Locatelli: Università di Parma

Journal of Global Optimization, 2018, vol. 72, issue 2, No 7, 277-303

Abstract: 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 $$x^n y^m$$ x n y m over boxes.

Keywords: Global optimization; Convex envelope; KKT conditions (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-018-0626-1

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