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A dual simplex-type algorithm for the smallest enclosing ball of balls

Author

Listed:
  • Marta Cavaleiro

    (Rutgers University
    University Heights)

  • Farid Alizadeh

    (Rutgers University)

Abstract

We develop a dual simplex-type algorithm for computing the smallest enclosing ball of a set of balls and other closely related problems. Our algorithm employs a pivoting scheme resembling the simplex method for linear programming, in which a sequence of exact curve searches is performed until a new dual feasible solution with a strictly smaller objective function value is found. We utilize the Cholesky factorization and procedures for updating it, yielding a numerically stable implementation of the algorithm. We show that our algorithm can efficiently solve instances of dimension 5000 with 100000 points, often within minutes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:79:y:2021:i:3:d:10.1007_s10589-021-00283-6
    DOI: 10.1007/s10589-021-00283-6
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    References listed on IDEAS

    as
    1. Nguyen Mau Nam & Nguyen Hoang & Nguyen Thai An, 2014. "Constructions of Solutions to Generalized Sylvester and Fermat–Torricelli Problems for Euclidean Balls," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 483-509, February.
    2. Trevor Hale & Christopher Moberg, 2003. "Location Science Research: A Review," Annals of Operations Research, Springer, vol. 123(1), pages 21-35, October.
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    Cited by:

    1. 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.
    2. 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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