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Finiteness Result for the Simplicial Branch-and-Bound Algorithm Based on ω-Subdivisions

Author

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  • M. Locatelli

    (Universitá di Torino)

  • U. Raber

    (University of Trier)

Abstract

The question of the finiteness of simplicial branch-and-bound algorithms employing only ω-subdivisions is considered. In Ref. 1, it was shown that this algorithm is convergent; here, it is proved that the algorithm is also finite if two assumptions are fulfilled. The first assumption requires the function values at vertices of the initial simplex to be lower than the optimal value of the problem. The second assumption requires each vertex of the initial simplex to violate at most one of the constraints defining the feasible polytope. The first assumption is mild from a theoretical point of view; the second assumption is strong, but holds always for instance when the feasible region is a hypercube.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:1:d:10.1023_a:1004656716776
    DOI: 10.1023/A:1004656716776
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    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. 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.
    3. Takahito Kuno & Paul Buckland, 2012. "A convergent simplicial algorithm with ω-subdivision and ω-bisection strategies," Journal of Global Optimization, Springer, vol. 52(3), pages 371-390, March.

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    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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