On the exhaustivity of simplicial partitioning

Authors:
Peter J. Dickinson
Affiliations:
Johann Bernoulli Institute, University of Groningen, Groningen, The Netherlands 9700 AK
Venue:
Journal of Global Optimization
Year:
2014

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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.