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The Weiszfeld Algorithm: Proof, Amendments, and Extensions

In: Foundations of Location Analysis

Author

Listed:
  • Frank Plastria

    (Vrije Universiteit Brussel)

Abstract

Some time in the early seventeenth century, the following geometrical optimization problem was posed:

Suggested Citation

  • Frank Plastria, 2011. "The Weiszfeld Algorithm: Proof, Amendments, and Extensions," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Foundations of Location Analysis, chapter 0, pages 357-389, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-7572-0_16
    DOI: 10.1007/978-1-4419-7572-0_16
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    Citations

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    Cited by:

    1. Plastria, Frank, 2016. "How bad can the centroid be?," European Journal of Operational Research, Elsevier, vol. 252(1), pages 98-102.
    2. Tom Blockmans & Marie-Anne Guerry, 2015. "Probabilistic Spatial Power Indexes: The Impact of Issue Saliences and Distance Selection," Group Decision and Negotiation, Springer, vol. 24(4), pages 675-697, July.
    3. Tom Blockmans & Marie-Anne Guerry, 2016. "Coalition Formation Procedures: The Impact of Issue Saliences and Consensus Estimation," Group Decision and Negotiation, Springer, vol. 25(3), pages 481-499, May.
    4. Jianlin Jiang & Liyun Ling & Yan Gu & Su Zhang & Yibing Lv, 2023. "Customized Alternating Direction Methods of Multipliers for Generalized Multi-facility Weber Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 362-389, January.
    5. 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.
    6. Marianov, Vladimir & Eiselt, H.A., 2024. "Fifty Years of Location Theory - A Selective Review," European Journal of Operational Research, Elsevier, vol. 318(3), pages 701-718.
    7. 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.
    8. 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.
    9. 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.

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