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A Branch-and-Bound Approach for Estimating Covering Functionals of Convex Bodies

Author

Listed:
  • Chan He

    (North University of China)

  • Yafang Lv

    (North University of China)

  • Horst Martini

    (Technische Universität Chemnitz)

  • Senlin Wu

    (North University of China)

Abstract

Estimating covering functionals of convex bodies is not only interesting for its own, but also an important part of Chuanming Zong’s program to attack Hadwiger’s covering conjecture, a long-standing open problem from Discrete and Combinatorial Geometry. In general, it is difficult to determine exact values of the covering functionals of a convex body by theoretical analysis. Therefore we propose a global optimization algorithm based on the geometric branch-and-bound method. Numerical experiments have been carried out to estimate covering functionals of the Euclidean unit disc.

Suggested Citation

  • Chan He & Yafang Lv & Horst Martini & Senlin Wu, 2023. "A Branch-and-Bound Approach for Estimating Covering Functionals of Convex Bodies," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1036-1055, March.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:3:d:10.1007_s10957-022-02146-4
    DOI: 10.1007/s10957-022-02146-4
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    References listed on IDEAS

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    1. Zvi Drezner & Atsuo Suzuki, 2004. "The Big Triangle Small Triangle Method for the Solution of Nonconvex Facility Location Problems," Operations Research, INFORMS, vol. 52(1), pages 128-135, February.
    2. Plastria, Frank, 1992. "GBSSS: The generalized big square small square method for planar single-facility location," European Journal of Operational Research, Elsevier, vol. 62(2), pages 163-174, October.
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    Cited by:

    1. Man Yu & Yafang Lv & Yanping Zhao & Chan He & Senlin Wu, 2023. "Estimations of Covering Functionals of Convex Bodies Based on Relaxation Algorithm," Mathematics, MDPI, vol. 11(9), pages 1-15, April.

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