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Location Problems with Different Norms for Different Points

Author

Listed:
  • P. L. Papini

    (University of Bologna)

  • J. Puerto

    (University of Seville)

Abstract

Given a finite set $$A=\{a_1,\dots,{a_n}\}$$ in a linear space X, we consider two problems. The first problem consists of finding the points minimizing the maximum distance to the points in A; the second problem looks for the points that minimize the average distance to the points in A. In both cases, we assume that the distances at different points are defined as $$ d(x,{a_i})=\|x-{a_i}\|_i,\quad for i=1,\dots,n, $$ with norms $$\|\cdot \|_i$$ defined on X. The use of different norms to measure distances from different points allows us to extend some results that hold in the single-norm case, while some strange and rather unexpected facts arise in the general case.

Suggested Citation

  • P. L. Papini & J. Puerto, 2005. "Location Problems with Different Norms for Different Points," Journal of Optimization Theory and Applications, Springer, vol. 125(3), pages 673-695, June.
    • Handle: RePEc:spr:joptap:v:125:y:2005:i:3:d:10.1007_s10957-005-2095-1
    DOI: 10.1007/s10957-005-2095-1
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    Cited by:

    1. Frank Plastria, 2009. "Asymmetric distances, semidirected networks and majority in Fermat–Weber problems," Annals of Operations Research, Springer, vol. 167(1), pages 121-155, March.
    2. Frank Plastria, 2021. "Using the power of ideal solutions: simple proofs of some old and new results in location theory," 4OR, Springer, vol. 19(3), pages 449-467, September.

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