Polyhedral subdivisions and functional forms for the convex envelopes of bilinear, fractional and other bivariate functions over general polytopes

Marco Locatelli ()
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Marco Locatelli: Università di Parma

Journal of Global Optimization, 2016, vol. 66, issue 4, No 3, 629-668

Abstract: Abstract In this paper we show that the convex envelope over polytopes for a class of bivariate functions, including the bilinear and fractional functions as special cases, is characterized by a polyhedral subdivision of the polytopes, and is such that over each member of the subdivision the convex envelope has a given (although possibly only implicitly defined) functional form. For the bilinear and fractional case we show that there are three possible functional forms, which can be explicitly defined.

Keywords: Convex envelopes; Polyhedral subdivisions; Bilinear terms; Fractional terms (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-016-0418-4

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