Journal
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
Volume 27, Issue 1, Pages 5-22Publisher
KLUWER ACADEMIC PUBL
DOI: 10.1023/B:COAP.0000004976.52180.7f
Keywords
convex envelope; bilinear programming; fractional programming; global optimization
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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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