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A dual algorithm for the minimum covering weighted ball problem in $${\mathbb{R}^n}$$

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  • P. Dearing
  • Andrea Smith

Abstract

The nonlinear convex programming problem of finding the minimum covering weighted ball of a given finite set of points in $${\mathbb{R}^n}$$ is solved by generating a finite sequence of subsets of the points and by finding the minimum covering weighted ball of each subset in the sequence until all points are covered. Each subset has at most n + 1 points and is affinely independent. The radii of the covering weighted balls are strictly increasing. The minimum covering weighted ball of each subset is found by using a directional search along either a ray or a circular arc, starting at the solution to the previous subset. The step size is computed explicitly at each iteration. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • P. Dearing & Andrea Smith, 2013. "A dual algorithm for the minimum covering weighted ball problem in $${\mathbb{R}^n}$$," Journal of Global Optimization, Springer, vol. 55(2), pages 261-278, February.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:2:p:261-278
    DOI: 10.1007/s10898-011-9796-9
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    References listed on IDEAS

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    1. Nimrod Megiddo, 1983. "The Weighted Euclidean 1-Center Problem," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 498-504, November.
    2. Donald W. Hearn & James Vijay, 1982. "Efficient Algorithms for the (Weighted) Minimum Circle Problem," Operations Research, INFORMS, vol. 30(4), pages 777-795, August.
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