Regular simplex refinement by regular simplices

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