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

  • Authors:

  • Harold P. Benson

  • Affiliations:

  • Warrington College of Business Administration, University of Florida, Gainesville, Florida, USA. harold.benson@cba.ufl.edu

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 2004

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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.