On the Exhaustivity of Simplicial Partitioning

Peter James Clair Dickinson

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

Abstract

During the last 40 years, simplicial partitioning has been shown to be highly useful, including in the field of nonlinear optimization, specifically global optimization. In this article, we consider results on the exhaustivity of simplicial partitioning schemes. We consider conjectures on this exhaustivity which seem at first glance to be true (two of which have been stated as true in published articles). However, we will provide counter-examples to these conjectures. We also provide a new simplicial partitioning scheme, which provides a lot of freedom, whilst guaranteeing exhaustivity.
Original languageUndefined
Pages (from-to)189-203
Number of pages15
JournalJournal of global optimization
Volume58
Issue number1
DOIs
Publication statusPublished - Jan 2014

Keywords

  • EWI-25478
  • MSC-65K99
  • MSC-90C26
  • Nonconvex programming
  • IR-94365
  • Partitioning
  • Exhaustivity
  • METIS-309762
  • Simplices

Cite this

Dickinson, Peter James Clair. / On the Exhaustivity of Simplicial Partitioning. In: Journal of global optimization. 2014 ; Vol. 58, No. 1. pp. 189-203.
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On the Exhaustivity of Simplicial Partitioning. / Dickinson, Peter James Clair.

In: Journal of global optimization, Vol. 58, No. 1, 01.2014, p. 189-203.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - During the last 40 years, simplicial partitioning has been shown to be highly useful, including in the field of nonlinear optimization, specifically global optimization. In this article, we consider results on the exhaustivity of simplicial partitioning schemes. We consider conjectures on this exhaustivity which seem at first glance to be true (two of which have been stated as true in published articles). However, we will provide counter-examples to these conjectures. We also provide a new simplicial partitioning scheme, which provides a lot of freedom, whilst guaranteeing exhaustivity.

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KW - MSC-65K99

KW - MSC-90C26

KW - Nonconvex programming

KW - IR-94365

KW - Partitioning

KW - Exhaustivity

KW - METIS-309762

KW - Simplices

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