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On Convergence of the Simplicial Branch-and-Bound Algorithm Based on ω-Subdivisions

Author

Listed:
  • M. Locatelli

    (Universitá di Torino)

  • U. Raber

    (University of Trier)

Abstract

The problem of minimizing a concave function over a polytope is considered. The simplicial branch-and-bound approach is presented and theoretical studies about the convergence of these algorithms are carried on. In particular, the convergence of the algorithm based on so-called ω-subdivisions is proved, which had been an open question for a long time.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:1:d:10.1023_a:1004604732705
    DOI: 10.1023/A:1004604732705
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    References listed on IDEAS

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    1. James E. Falk & Richard M. Soland, 1969. "An Algorithm for Separable Nonconvex Programming Problems," Management Science, INFORMS, vol. 15(9), pages 550-569, May.
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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.
    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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