Journal
MATHEMATICAL PROGRAMMING
Volume 103, Issue 2, Pages 207-224Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-005-0580-9
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Deterministic global optimization algorithms frequently rely on the convex underestimation of nonconvex functions. In this paper we describe the structure of the polyhedral convex envelopes of edge-concave functions over polyhedral domains using geometric arguments. An algorithm for computing the facets of the convex envelope over hyperrectangles in R-3 is described. Sufficient conditions are described under which the convex envelope of a sum of edge-concave functions may be shown to be equivalent to the sum of the convex envelopes of these functions.
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