Regular simplex refinement by regular simplices

L.G. Casado, B.G. Tóth, E.M.T. Hendrix, I. García

Research output: Chapter in Book/Report/Conference proceedingConference paper

Abstract

A naturalway to define branching in Branch-and-Bound for blending problemis to do bisection. The disadvantage of bisectioning is that partition sets are in general irregular. A regular simplex with fixed orientation can be determined by its center and size, allowing storage savings in a Branchand- Bound algorithm from computational perspective. Unfortunately for dimension n>3 a regular simplex cannot be covered by regular subsimplices without overlapping. The possible difficulties of the refinement by regular simplices are studied here. The main challenge is to find a refinement with a good convergence ratio which facilitates the discarding of simplices in an overlapped and already evaluated region.
Original languageEnglish
Title of host publicationProceedings of the XII Global Optimization Workshop MAGO 2014 Mathematical and applied global optimization
EditorsL.G. Casado, I. García, E.M.T. Hendrix
PublisherUniversidad de Almería
Pages93-96
ISBN (Print)9788416027576
Publication statusPublished - 2014
EventMAGO 2014, Málaga, Spain -
Duration: 1 Sep 20144 Sep 2014

Conference

ConferenceMAGO 2014, Málaga, Spain
Period1/09/144/09/14

Cite this

Casado, L. G., Tóth, B. G., Hendrix, E. M. T., & García, I. (2014). Regular simplex refinement by regular simplices. In L. G. Casado, I. García, & E. M. T. Hendrix (Eds.), Proceedings of the XII Global Optimization Workshop MAGO 2014 Mathematical and applied global optimization (pp. 93-96). Universidad de Almería. http://www.hpca.ual.es/~MAGO14/MAGO14-Proceedings.pdf#page=102