IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v53y2012i1p115-130.html
   My bibliography  Save this article

The nearest point problem in a polyhedral set and its extensions

Author

Listed:
  • Zhe Liu
  • Yahya Fathi

Abstract

In this paper we investigate the relationship between the nearest point problem in a polyhedral cone and the nearest point problem in a polyhedral set, and use this relationship to devise an effective method for solving the latter using an existing algorithm for the former. We then show that this approach can be employed to minimize any strictly convex quadratic function over a polyhedral set. Through a computational experiment we evaluate the effectiveness of this approach and show that for a collection of randomly generated instances this approach is more effective than other existing methods for solving these problems. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Zhe Liu & Yahya Fathi, 2012. "The nearest point problem in a polyhedral set and its extensions," Computational Optimization and Applications, Springer, vol. 53(1), pages 115-130, September.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:1:p:115-130
    DOI: 10.1007/s10589-011-9448-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-011-9448-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-011-9448-5?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. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    2. Zhe Liu & Yahya Fathi, 2011. "An active index algorithm for the nearest point problem in a polyhedral cone," Computational Optimization and Applications, Springer, vol. 49(3), pages 435-456, July.
    3. V. Ruggiero & L. Zanni, 2000. "A Modified Projection Algorithm for Large Strictly-Convex Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 255-279, February.
    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. Zhe Liu & Yahya Fathi, 2011. "An active index algorithm for the nearest point problem in a polyhedral cone," Computational Optimization and Applications, Springer, vol. 49(3), pages 435-456, July.
    2. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2005. "Computing Integral Solutions of Complementarity Problems," Discussion Paper 2005-5, Tilburg University, Center for Economic Research.
    3. Zhang, Bin, 2012. "Multi-tier binary solution method for multi-product newsvendor problem with multiple constraints," European Journal of Operational Research, Elsevier, vol. 218(2), pages 426-434.
    4. Baohua Huang & Wen Li, 2023. "A smoothing Newton method based on the modulus equation for a class of weakly nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 86(1), pages 345-381, September.
    5. Talman, A.J.J. & van der Heyden, L., 1981. "Algorithms for the linear complementarity problem which allow an arbitrary starting point," Research Memorandum FEW 99, Tilburg University, School of Economics and Management.
    6. Bernhard von Stengel & Antoon van den Elzen & Dolf Talman, 2002. "Computing Normal Form Perfect Equilibria for Extensive Two-Person Games," Econometrica, Econometric Society, vol. 70(2), pages 693-715, March.
    7. Christian Bidard, 2012. "The Frail Grounds of the Ricardian Dynamics," Working Papers hal-04141039, HAL.
    8. R. B. Bapat & S. K. Neogy, 2016. "On a quadratic programming problem involving distances in trees," Annals of Operations Research, Springer, vol. 243(1), pages 365-373, August.
    9. Frederic Murphy & Axel Pierru & Yves Smeers, 2016. "A Tutorial on Building Policy Models as Mixed-Complementarity Problems," Interfaces, INFORMS, vol. 46(6), pages 465-481, December.
    10. Richard Asmuth, 1978. "Studying Economic Equilibria on Affine Networks Via Lemke's Algorithm," Discussion Papers 314, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
    12. Benjamin F. Hobbs & J. S. Pang, 2007. "Nash-Cournot Equilibria in Electric Power Markets with Piecewise Linear Demand Functions and Joint Constraints," Operations Research, INFORMS, vol. 55(1), pages 113-127, February.
    13. Rahul Savani & Bernhard von Stengel, 2016. "Unit vector games," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(1), pages 7-27, March.
    14. V. Venkateswaran, 1991. "A descent approach to solving the complementary programming problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 679-698, October.
    15. Murray, Timothy & Garg, Jugal & Nagi, Rakesh, 2021. "Limited-trust equilibria," European Journal of Operational Research, Elsevier, vol. 289(1), pages 364-380.
    16. Peter Godfrey-Smith & Manolo Martínez, 2013. "Communication and Common Interest," PLOS Computational Biology, Public Library of Science, vol. 9(11), pages 1-6, November.
    17. S. R. Mohan, 1997. "Degeneracy Subgraph of the Lemke Complementary Pivot Algorithm and Anticycling Rule," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 409-423, August.
    18. Bidard, Christian, 2014. "The Ricardian rent theory: an overview," Centro Sraffa Working Papers CSWP8, Centro di Ricerche e Documentazione "Piero Sraffa".
    19. Bahrami, Sina & Roorda, Matthew J., 2020. "Optimal traffic management policies for mixed human and automated traffic flows," Transportation Research Part A: Policy and Practice, Elsevier, vol. 135(C), pages 130-143.
    20. Harry M. Markowitz, 2002. "Efficient Portfolios, Sparse Matrices, and Entities: A Retrospective," Operations Research, INFORMS, vol. 50(1), pages 154-160, February.

    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:coopap:v:53:y:2012:i:1:p:115-130. 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.