AbsTaylor: Finding inner regions for nonlinear constraint systems with linearizations and absolute values

Ignacio Araya, Victor Reyes

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this paper we propose a simple and cheap method for extracting inner polytopes, i.e., entirely feasible convex regions in which all points satisfy the constraints. The method performs an inner linearization of a set of nonlinear constraints by using a Taylor form. Unlike a previous proposal, the expansion point of the Taylor form is not limited to the bounds of the domains; it can be given by any point inside the studied region producing, in general, a tighter approximation. The approach was used as an upper bounding method in a state-of-The-Art global branch & bound optimizer. In the studied instances, the new method finds in average much more inner regions (in 20% of the processed nodes) than the original approach (in 5% of the nodes).

Original languageEnglish
Title of host publicationProceedings LeGO 2018 � 14th International Global Optimization Workshop
EditorsAndre H. Deutz, Sander C. Hille, Yaroslav D. Sergeyev, Michael T. M. Emmerich
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735417984
DOIs
StatePublished - 12 Feb 2019
Externally publishedYes
Event14th International Global Optimization Workshop, LeGO 2018 - Leiden, Netherlands
Duration: 18 Sep 201821 Sep 2018

Publication series

NameAIP Conference Proceedings
Volume2070
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference14th International Global Optimization Workshop, LeGO 2018
Country/TerritoryNetherlands
CityLeiden
Period18/09/1821/09/18

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