### 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 language | English |
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Title of host publication | Proceedings of the XII Global Optimization Workshop MAGO 2014 Mathematical and applied global optimization |

Editors | L.G. Casado, I. García, E.M.T. Hendrix |

Publisher | Universidad de Almería |

Pages | 93-96 |

ISBN (Print) | 9788416027576 |

Publication status | Published - 2014 |

Event | MAGO 2014, Málaga, Spain - Duration: 1 Sep 2014 → 4 Sep 2014 |

### Conference

Conference | MAGO 2014, Málaga, Spain |
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Period | 1/09/14 → 4/09/14 |

## 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