IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v24y2016i2d10.1007_s11750-015-0405-9.html
   My bibliography  Save this article

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

Author

Listed:
  • P. M. Dearing

    (Clemson University)

  • Pietro Belotti

    (Xpress Optimization team)

  • Andrea M. Smith

    (Liberty University)

Abstract

The nonlinear programming problem of finding the minimum covering ball of a finite set of points in $$\mathbb {R}^n$$ R n , with a positive weight corresponding to each point, is solved by a directional search method. At each iteration, the search path is either a ray or the arc of a circle and is determined by bisectors of points. Each step size along the search path is determined explicitly. The primal algorithm is shown to search along the farthest point Voronoi diagram of the given points. We provide computational results that show the efficiency of the algorithm when compared to general convex nonlinear optimization solvers.

Suggested Citation

  • P. M. Dearing & Pietro Belotti & Andrea M. Smith, 2016. "A primal algorithm for the weighted minimum covering ball problem in $$\mathbb {R}^n$$ R n," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 466-492, July.
    • Handle: RePEc:spr:topjnl:v:24:y:2016:i:2:d:10.1007_s11750-015-0405-9
    DOI: 10.1007/s11750-015-0405-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-015-0405-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11750-015-0405-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Donald W. Hearn & James Vijay, 1982. "Efficient Algorithms for the (Weighted) Minimum Circle Problem," Operations Research, INFORMS, vol. 30(4), pages 777-795, August.
    2. Robert G. Bland, 1977. "New Finite Pivoting Rules for the Simplex Method," Mathematics of Operations Research, INFORMS, vol. 2(2), pages 103-107, May.
    3. BLAND, Robert G., 1977. "New finite pivoting rules for the simplex method," LIDAM Reprints CORE 315, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Omer, Jérémy & Soumis, François, 2015. "A linear programming decomposition focusing on the span of the nondegenerate columns," European Journal of Operational Research, Elsevier, vol. 245(2), pages 371-383.
    2. Csizmadia, Zsolt & Illés, Tibor & Nagy, Adrienn, 2012. "The s-monotone index selection rules for pivot algorithms of linear programming," European Journal of Operational Research, Elsevier, vol. 221(3), pages 491-500.
    3. Filippi, Carlo & Romanin-Jacur, Giorgio, 2002. "Multiparametric demand transportation problem," European Journal of Operational Research, Elsevier, vol. 139(2), pages 206-219, June.
    4. Fabio Vitor & Todd Easton, 2018. "The double pivot simplex method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 109-137, February.
    5. Adrienn Csizmadia & Zsolt Csizmadia & Tibor Illés, 2018. "Finiteness of the quadratic primal simplex method when s-monotone index selection rules are applied," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 535-550, September.
    6. Im, Haesol & Wolkowicz, Henry, 2023. "Revisiting degeneracy, strict feasibility, stability, in linear programming," European Journal of Operational Research, Elsevier, vol. 310(2), pages 495-510.
    7. Jean Bertrand Gauthier & Jacques Desrosiers & Marco E. Lübbecke, 2016. "Tools for primal degenerate linear programs: IPS, DCA, and PE," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(2), pages 161-204, June.
    8. Pan, Ping-Qi, 2008. "A largest-distance pivot rule for the simplex algorithm," European Journal of Operational Research, Elsevier, vol. 187(2), pages 393-402, June.
    9. Magnanti, Thomas L. & Orlin, James B., 1953-., 1985. "Parametric linear programming and anti-cycling pivoting rules," Working papers 1730-85., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    10. Michael J. Best & Xili Zhang, 2011. "Degeneracy Resolution for Bilinear Utility Functions," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 615-634, September.
    11. K. O. Kortanek & Zhu Jishan, 1988. "New purification algorithms for linear programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(4), pages 571-583, August.
    12. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.
    13. Osman Ou{g}uz, 2002. "Generalized Column Generation for Linear Programming," Management Science, INFORMS, vol. 48(3), pages 444-452, March.
    14. Illes, Tibor & Terlaky, Tamas, 2002. "Pivot versus interior point methods: Pros and cons," European Journal of Operational Research, Elsevier, vol. 140(2), pages 170-190, July.
    15. Issmail Elhallaoui & Abdelmoutalib Metrane & Guy Desaulniers & François Soumis, 2011. "An Improved Primal Simplex Algorithm for Degenerate Linear Programs," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 569-577, November.
    16. Liu, Yanwu & Tu, Yan & Zhang, Zhongzhen, 2021. "The row pivoting method for linear programming," Omega, Elsevier, vol. 100(C).
    17. Xiaoyin Hu & Jianshu Li & Xiaoya Li & Jinchuan Cui, 2020. "A Revised Inverse Data Envelopment Analysis Model Based on Radial Models," Mathematics, MDPI, vol. 8(5), pages 1-17, May.
    18. Zhang, Shuzhong, 1999. "New variants of finite criss-cross pivot algorithms for linear programming," European Journal of Operational Research, Elsevier, vol. 116(3), pages 607-614, August.
    19. John W. Mamer & Richard D. McBride, 2000. "A Decomposition-Based Pricing Procedure for Large-Scale Linear Programs: An Application to the Linear Multicommodity Flow Problem," Management Science, INFORMS, vol. 46(5), pages 693-709, May.
    20. Zvi Drezner & G. O. Wesolowsky, 1991. "Facility location when demand is time dependent," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 763-777, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:topjnl:v:24:y:2016:i:2:d:10.1007_s11750-015-0405-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.