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

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  • Takahito Kuno

    (University of Tsukuba)

  • Tomohiro Ishihama

    (NS Solutions Corporation)

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.

Suggested Citation

  • Takahito Kuno & Tomohiro Ishihama, 2016. "A generalization of $$\omega $$ ω -subdivision ensuring convergence of the simplicial algorithm," Computational Optimization and Applications, Springer, vol. 64(2), pages 535-555, June.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:2:d:10.1007_s10589-015-9817-6
    DOI: 10.1007/s10589-015-9817-6
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    References listed on IDEAS

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    1. Nguyen Van Thoai & Hoang Tuy, 1980. "Convergent Algorithms for Minimizing a Concave Function," Mathematics of Operations Research, INFORMS, vol. 5(4), pages 556-566, November.
    2. M. Locatelli & U. Raber, 2000. "Finiteness Result for the Simplicial Branch-and-Bound Algorithm Based on ω-Subdivisions," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 81-88, October.
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    Cited by:

    1. Takahito Kuno, 2018. "A modified simplicial algorithm for convex maximization based on an extension of $$\omega $$ ω -subdivision," Journal of Global Optimization, Springer, vol. 71(2), pages 297-311, June.

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