@inbook{e8e7a0361b784e50b4817205e6f944e3,
title = "On the composition of convex envelopes for quadrilinear terms",
abstract = "Within the framework of the spatial Branch-and-Bound algorithm for solving mixed-integer nonlinear programs, different convex relaxations can be obtained for multilinear terms by applying associativity in different ways. The two groupings ((x1x2)x3)x4 and (x1x2x3)x4 of a quadrilinear term, for example, give rise to two different convex relaxations. In Cafieri et al. (J Global Optim 47:661-685, 2010) we prove that having fewer groupings of longer terms yields tighter convex relaxations. In this chapter we give an alternative proof of the same fact and perform a computational study to assess the impact of the tightened convex relaxation in a spatial Branch-and-Bound setting.",
keywords = "Convex relaxation, Global optimization, MINLP, Quadrilinear, Reformulation, Spatial Branch-and-Bound",
author = "Pietro Belotti and Sonia Cafieri and Jon Lee and Leo Liberti and Miller, \{Andrew J.\}",
note = "Publisher Copyright: {\textcopyright} Springer Science+Business Media New York 2013.",
year = "2013",
month = jan,
day = "1",
doi = "10.1007/978-1-4614-5131-0\_1",
language = "English",
series = "Springer Optimization and Its Applications",
publisher = "Springer International Publishing",
pages = "1--16",
booktitle = "Springer Optimization and Its Applications",
}