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Comparison of convex relaxations of quadrilinear terms

By Sonia Cafieri, Jon Lee and Leo Liberti


In this paper we compare four different ways to compute a convex linear relaxation of a quadrilinear monomial on a box, analyzing their relative tightness. We computationally compare the quality of the relaxations, and we provide a general theorem on pairwise-comparison of relaxation strength, which applies to some of our pairs of relaxations for quadrilinear monomials. Our results can be used to configure a spatial Branch-and-Bound global optimization algorithm. We apply our results to the Molecular Distance Geometry Problem, demonstrating the usefulness of the present study. quadrilinear; convex relaxation; reformulation; global optimization, spatial Branch

Year: 2010
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