Regular simplex refinement by regular simplices
2014
Casado, L.G. | Tóth, B.G. | Hendrix, E.M.T. | García, I.
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.
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