A generalization of $$\omega $$ ω -subdivision ensuring convergence of the simplicial algorithm

Takahito Kuno () and Tomohiro Ishihama
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Takahito Kuno: University of Tsukuba
Tomohiro Ishihama: NS Solutions Corporation

Computational Optimization and Applications, 2016, vol. 64, issue 2, No 9, 535-555

Abstract: Abstract In this paper, we refine the proof of convergence by Kuno–Buckland (J Global Optim 52:371–390, 2012) for the simplicial algorithm with $$\omega $$ ω -subdivision and generalize their $$\omega $$ ω -bisection rule to establish a class of subdivision rules, called $$\omega $$ 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 $$\omega $$ ω -k-section rule with the usual $$\omega $$ ω -subdivision rule.

Keywords: Global optimization; Strictly convex maximization; Branch-and-bound; Simplicial algorithm; $$\omega $$ ω -subdivision (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10589-015-9817-6

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