Skip to Main content Skip to Navigation
Book sections

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.
Document type :
Book sections
Complete list of metadatas

Cited literature [30 references]  Display  Hide  Download
Contributor : Andrew J. Miller <>
Submitted on : Wednesday, January 2, 2013 - 11:17:14 PM
Last modification on : Wednesday, May 6, 2020 - 5:44:10 PM
Document(s) archivé(s) le : Wednesday, April 3, 2013 - 3:49:20 AM


Files produced by the author(s)




Pietro Belotti, Sonia Cafieri, Jon Lee, Leo Liberti, Andrew J. Miller. On the composition of convex envelopes for quadrilinear terms. Optimization, Simulation, and Control, Springer Verlag, pp 1-16, 2013, Springer Optimization and Its Applications, Volume 76, 978-1-4614-5130-3. ⟨10.1007/978-1-4614-5131-0_1⟩. ⟨hal-00769671⟩



Record views


Files downloads