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On the point for which the sum of the distances to n given points is minimum

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  • E. Weiszfeld
  • Frank Plastria

Abstract

Translation with annotations of E. Weiszfeld, Sur le point pour lequel la somme des distances de n points donnés est minimum, Tôhoku Mathematical Journal (first series), 43 (1937) pp. 355–386. A short introduction about the translation is found in Appendix A. Appendix B lists particular notations used by Weiszfeld and their now more conventional equivalents. Numbered footnotes are those of the original paper of Weiszfeld. Boxed numerals are references to observations about the translation and comments of the translator, all to be found in Appendix C. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • E. Weiszfeld & Frank Plastria, 2009. "On the point for which the sum of the distances to n given points is minimum," Annals of Operations Research, Springer, vol. 167(1), pages 7-41, March.
    • Handle: RePEc:spr:annopr:v:167:y:2009:i:1:p:7-41:10.1007/s10479-008-0352-z
    DOI: 10.1007/s10479-008-0352-z
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    Cited by:

    1. Vinué, Guillermo, 2017. "Anthropometry: An R Package for Analysis of Anthropometric Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 77(i06).
    2. Boris Mordukhovich & Nguyen Mau Nam, 2011. "Applications of Variational Analysis to a Generalized Fermat-Torricelli Problem," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 431-454, March.
    3. Zvi Drezner & Mozart B. C. Menezes, 2016. "The wisdom of voters: evaluating the Weber objective in the plane at the Condorcet solution," Annals of Operations Research, Springer, vol. 246(1), pages 205-226, November.
    4. Tammy Drezner & Zvi Drezner, 2016. "Sequential location of two facilities: comparing random to optimal location of the first facility," Annals of Operations Research, Springer, vol. 246(1), pages 5-18, November.
    5. Plastria, Frank, 2016. "How bad can the centroid be?," European Journal of Operational Research, Elsevier, vol. 252(1), pages 98-102.
    6. Frank Plastria & Tom Blockmans, 2015. "Multidimensional Theoretic Consensus Reachability: The Impact of Distance Selection and Issue Saliences," Group Decision and Negotiation, Springer, vol. 24(1), pages 1-44, January.
    7. 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.
    8. Murray, Alan T. & Church, Richard L. & Feng, Xin, 2020. "Single facility siting involving allocation decisions," European Journal of Operational Research, Elsevier, vol. 284(3), pages 834-846.
    9. Frank Plastria, 2016. "Up- and downgrading the euclidean 1-median problem and knapsack Voronoi diagrams," Annals of Operations Research, Springer, vol. 246(1), pages 227-251, November.
    10. Zvi Drezner & Carlton Scott, 2013. "Location of a distribution center for a perishable product," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(3), pages 301-314, December.
    11. Amir Beck & Shoham Sabach, 2015. "Weiszfeld’s Method: Old and New Results," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 1-40, January.
    12. Rodríguez-Chía, Antonio M. & Espejo, Inmaculada & Drezner, Zvi, 2010. "On solving the planar k-centrum problem with Euclidean distances," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1169-1186, December.
    13. Jiwon Baik & Alan T. Murray, 2022. "Locating a facility to simultaneously address access and coverage goals," Papers in Regional Science, Wiley Blackwell, vol. 101(5), pages 1199-1217, October.
    14. David Degras, 2021. "Sparse group fused lasso for model segmentation: a hybrid approach," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(3), pages 625-671, September.
    15. Dürre, Alexander & Vogel, Daniel & Tyler, David E., 2014. "The spatial sign covariance matrix with unknown location," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 107-117.
    16. Simeon Reich & Truong Minh Tuyen, 2023. "The Generalized Fermat–Torricelli Problem in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 78-97, January.
    17. Frank Plastria & Mohamed Elosmani, 2013. "Continuous location of an assembly station," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 323-340, July.
    18. F. Plastria, 2014. "Improved fixed point optimality conditions for mixed norms minisum location," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 170-184, April.
    19. M. Akyüz & İ. Altınel & Temel Öncan, 2014. "Location and allocation based branch and bound algorithms for the capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 222(1), pages 45-71, November.

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