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On the Construction of Convex and Concave Envelope Formulas for Bilinear and Fractional Functions on Quadrilaterals

Computational Optimization and Applications volume 27, pages 5–22 (2004)Cite this article

Abstract

Convex and concave envelopes play important roles in various types of optimization problems. In this article, we present a result that gives general guidelines for constructing convex and concave envelopes of functions of two variables on bounded quadrilaterals. We show how one can use this result to construct convex and concave envelopes of bilinear and fractional functions on rectangles, parallelograms and trapezoids. Applications of these results to global optimization are indicated.

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Authors and Affiliations

  1. Warrington College of Business Administration, University of Florida, Gainesville, Florida, USA

    Harold P. Benson

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  1. Harold P. Benson
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Benson, H.P. On the Construction of Convex and Concave Envelope Formulas for Bilinear and Fractional Functions on Quadrilaterals. Computational Optimization and Applications 27, 5–22 (2004). https://doi.org/10.1023/B:COAP.0000004976.52180.7f

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  • DOI: https://doi.org/10.1023/B:COAP.0000004976.52180.7f

  • convex envelope
  • bilinear programming
  • fractional programming
  • global optimization