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The minimum covering Euclidean ball of a set of Euclidean balls in $$I\!\!R^n$$ I R n

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  • P. M. Dearing

    (Clemson University)

  • Mark E. Cawood

    (Clemson University)

Abstract

Primal and dual algorithms are developed for solving the n-dimensional convex optimization problem of finding the Euclidean ball of minimum radius that covers m given Euclidean balls, each with given center and radius. Each algorithm is based on a directional search method in which a search path may be a ray or a two-dimensional conic section in $$I\!\!R^n$$ I R n . At each iteration, a search path is constructed by the intersection of bisectors of pairs of points, where the bisectors are either hyperplanes or n-dimensional hyperboloids. The optimal stopping point along each search path is determined explicitly.

Suggested Citation

  • P. M. Dearing & Mark E. Cawood, 2023. "The minimum covering Euclidean ball of a set of Euclidean balls in $$I\!\!R^n$$ I R n," Annals of Operations Research, Springer, vol. 322(2), pages 631-659, March.
    • Handle: RePEc:spr:annopr:v:322:y:2023:i:2:d:10.1007_s10479-022-05138-9
    DOI: 10.1007/s10479-022-05138-9
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    References listed on IDEAS

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    2. Marta Cavaleiro & Farid Alizadeh, 2021. "A dual simplex-type algorithm for the smallest enclosing ball of balls," Computational Optimization and Applications, Springer, vol. 79(3), pages 767-787, July.
    3. D. Jack Elzinga & Donald W. Hearn, 1972. "The Minimum Covering Sphere Problem," Management Science, INFORMS, vol. 19(1), pages 96-104, September.
    4. Nimrod Megiddo, 1983. "The Weighted Euclidean 1-Center Problem," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 498-504, November.
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    Cited by:

    1. Mark E. Cawood & P. M. Dearing, 2024. "The weighted Euclidean one-center problem in $${\mathbb {R}}^n$$ R n," Computational Optimization and Applications, Springer, vol. 89(2), pages 553-574, November.

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