IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v287y2020i2d10.1007_s10479-018-3018-5.html
   My bibliography  Save this article

On solving a non-convex quadratic programming problem involving resistance distances in graphs

Author

Listed:
  • Dipti Dubey

    (Indian Statistical Institute)

  • S. K. Neogy

    (Indian Statistical Institute)

Abstract

Quadratic programming problems involving distance matrix (D) that arises in trees are considered in the literature by Dankelmann (Discrete Math 312:12–20, 2012), Bapat and Neogy (Ann Oper Res 243:365–373, 2016). In this paper, we consider the question of solving the quadratic programming problem of finding maximum of $$x^{T}Rx$$xTRx subject to x being a nonnegative vector with sum 1 and show that for the class of simple graphs with resistance distance matrix (R) which are not necessarily a tree, this problem can be reformulated as a strictly convex quadratic programming problem. An application to symmetric bimatrix game is also presented.

Suggested Citation

  • Dipti Dubey & S. K. Neogy, 2020. "On solving a non-convex quadratic programming problem involving resistance distances in graphs," Annals of Operations Research, Springer, vol. 287(2), pages 643-651, April.
  • Handle: RePEc:spr:annopr:v:287:y:2020:i:2:d:10.1007_s10479-018-3018-5
    DOI: 10.1007/s10479-018-3018-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-018-3018-5
    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/s10479-018-3018-5?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. Éva Tardos, 1986. "A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs," Operations Research, INFORMS, vol. 34(2), pages 250-256, April.
    2. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    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. 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.
    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. Ting Pong & Hao Sun & Ningchuan Wang & Henry Wolkowicz, 2016. "Eigenvalue, quadratic programming, and semidefinite programming relaxations for a cut minimization problem," Computational Optimization and Applications, Springer, vol. 63(2), pages 333-364, March.
    5. 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.
    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. 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.
    9. Amitai Armon & Iftah Gamzu & Danny Segev, 2014. "Mobile facility location: combinatorial filtering via weighted occupancy," Journal of Combinatorial Optimization, Springer, vol. 28(2), pages 358-375, August.
    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. Balaji Gopalakrishnan & Seunghyun Kong & Earl Barnes & Ellis Johnson & Joel Sokol, 2011. "A least-squares minimum-cost network flow algorithm," Annals of Operations Research, Springer, vol. 186(1), pages 119-140, June.
    13. Clemens Heuberger, 2004. "Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 329-361, September.
    14. 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.
    15. 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.
    16. 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.
    17. Amitabh Basu & Jesús A. De Loera & Mark Junod, 2014. "On Chubanov's Method for Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 336-350, May.
    18. 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.
    19. Murray, Timothy & Garg, Jugal & Nagi, Rakesh, 2021. "Limited-trust equilibria," European Journal of Operational Research, Elsevier, vol. 289(1), pages 364-380.
    20. Peter Godfrey-Smith & Manolo Martínez, 2013. "Communication and Common Interest," PLOS Computational Biology, Public Library of Science, vol. 9(11), pages 1-6, November.

    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:annopr:v:287:y:2020:i:2:d:10.1007_s10479-018-3018-5. 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.