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A modified simplicial algorithm for convex maximization based on an extension of $$\omega $$ ω -subdivision

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  • Takahito Kuno

    (University of Tsukuba)

Abstract

The simplicial algorithm is a popular branch-and-bound approach to the convex maximization problem with multiple local maxima. In this paper, we discuss some difficulties revealed when implementing this algorithm under the $$\omega $$ ω -subdivision rule. To overcome those, we modify the bounding process and extend the $$\omega $$ ω -subdivision rule. We also report numerical results for the simplicial algorithm according to the new subdivision rule.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:2:d:10.1007_s10898-018-0619-0
    DOI: 10.1007/s10898-018-0619-0
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    References listed on IDEAS

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    1. 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.
    2. M. Locatelli & U. Raber, 2000. "On Convergence of the Simplicial Branch-and-Bound Algorithm Based on ω-Subdivisions," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 69-79, October.
    3. James E. Falk & Richard M. Soland, 1969. "An Algorithm for Separable Nonconvex Programming Problems," Management Science, INFORMS, vol. 15(9), pages 550-569, May.
    4. 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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