Journal Article A generalization of ω -subdivision ensuring convergence of the simplicial algorithm

Kuno, Takahito  ,  Ishihama, Tomohiro

64 ( 2 )  , pp.535 - 555 , 2016-06 , Springer US
In this paper, we refine the proof of convergence by Kuno–Buckland (J Global Optim 52:371–390, 2012) for the simplicial algorithm with ω-subdivision and generalize their ω-bisection rule to establish a class of subdivision rules, called ω-k-section, which bounds the number of subsimplices generated in a single execution of subdivision by a prescribed number k. We also report some numerical results of comparing the ω-k-section rule with the usual ω-subdivision rule.

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