Journal of Global Optimization
Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs
Optimization Methods & Software - GLOBAL OPTIMIZATION
A review of recent advances in global optimization
Journal of Global Optimization
Convex relaxation for solving posynomial programs
Journal of Global Optimization
Convex envelopes of products of convex and component-wise concave functions
Journal of Global Optimization
GloMIQO: Global mixed-integer quadratic optimizer
Journal of Global Optimization
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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 ℝ3 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.