On the Composition of Convex Envelopes for Quadrilinear Terms

Pietro Belotti (), Sonia Cafieri (), Jon Lee (), Leo Liberti () and Andrew J. Miller ()
Additional contact information
Pietro Belotti: Clemson University
Sonia Cafieri: Ecole Nationale de l’Aviation Civile
Jon Lee: University of Michigan
Leo Liberti: École Polytechnique
Andrew J. Miller: Université Bordeaux 1; RealOpt

A chapter in Optimization, Simulation, and Control, 2013, pp 1-16 from Springer

Abstract: 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 $$(({x}_{1}{x}_{2}){x}_{3}){x}_{4}$$ and $$({x}_{1}{x}_{2}{x}_{3}){x}_{4}$$ 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: Quadrilinear; Convex relaxation; Reformulation; Global optimization; Spatial Branch-and-Bound; MINLP (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations: View citations in EconPapers (3)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-5131-0_1

Ordering information: This item can be ordered from
http://www.springer.com/9781461451310

DOI: 10.1007/978-1-4614-5131-0_1

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().