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

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## 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## References

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