A generalization of \(\omega \)-subdivision ensuring convergence of the simplicial algorithm
In this paper, we refine the proof of convergence by Kuno–Buckland (J Global Optim 52:371–390, 2012) for the simplicial algorithm with \(\omega \)-subdivision and generalize their \(\omega \)-bisection rule to establish a class of subdivision rules, called \(\omega \)-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 \(\omega \)-k-section rule with the usual \(\omega \)-subdivision rule.
KeywordsGlobal optimization Strictly convex maximization Branch-and-bound Simplicial algorithm \(\omega \)-subdivision
The authors would like to thank the anonymous referees for their valuable comments, which significantly improved the quality of this article. Takahito Kuno was partially supported by a Grant-in-Aid for Scientific Research (C) 25330022 from the Japan Society for the Promotion of Sciences
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