IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v150y2011i1d10.1007_s10957-011-9821-7.html
   My bibliography  Save this article

Error Bounds for Nonlinear Complementarity Problems with Band Structure

Author

Listed:
  • Götz Alefeld

    (University of Karlsruhe (Karlsruhe Institute of Technology KIT))

  • Zhengyu Wang

    (Nanjing University)

Abstract

In this paper, we consider the nonlinear complementarity problem with band structure. This problem occurs, for example, if certain classes of free boundary problems are discretized. We compute error bounds for the approximate solution of the discretized problems. The error bounds are improved by an iterative method and can be made arbitrarily small. The ideas are illustrated by numerical experiments.

Suggested Citation

  • Götz Alefeld & Zhengyu Wang, 2011. "Error Bounds for Nonlinear Complementarity Problems with Band Structure," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 33-51, July.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:1:d:10.1007_s10957-011-9821-7
    DOI: 10.1007/s10957-011-9821-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-011-9821-7
    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/s10957-011-9821-7?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

    for a different version of it.

    References listed on IDEAS

    as
    1. B. Chen, 2001. "Error Bounds for R0-Type and Monotone Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 108(2), pages 297-316, February.
    2. Z.-Q. Luo & O. L. Mangasarian & J. Ren & M. V. Solodov, 1994. "New Error Bounds for the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 880-892, November.
    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. Yongchao Liu & Huifu Xu & Gui-Hua Lin, 2012. "Stability Analysis of One Stage Stochastic Mathematical Programs with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 537-555, February.
    2. Shouqiang Du & Weiyang Ding & Yimin Wei, 2021. "Acceptable Solutions and Backward Errors for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 260-276, January.
    3. M. V. Solodov, 1997. "Stationary Points of Bound Constrained Minimization Reformulations of Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 449-467, August.
    4. Chao Zhang & Xiaojun Chen & Naihua Xiu, 2009. "Global error bounds for the extended vertical LCP," Computational Optimization and Applications, Springer, vol. 42(3), pages 335-352, April.
    5. Coralia Cartis & Yiming Yan, 2016. "Active-set prediction for interior point methods using controlled perturbations," Computational Optimization and Applications, Springer, vol. 63(3), pages 639-684, April.
    6. Coralia Cartis & Yiming Yan, 2016. "Active-set prediction for interior point methods using controlled perturbations," Computational Optimization and Applications, Springer, vol. 63(3), pages 639-684, April.
    7. Shuhuang Xiang & Xiaojun Chen, 2011. "Computation of generalized differentials in nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 50(2), pages 403-423, October.
    8. M. V. Solodov, 1997. "Convergence Analysis of Perturbed Feasible Descent Methods," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 337-353, May.
    9. C. Zhang & X. Chen, 2008. "Stochastic Nonlinear Complementarity Problem and Applications to Traffic Equilibrium under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 277-295, May.
    10. C. Kanzow & N. Yamashita & M. Fukushima, 1997. "New NCP-Functions and Their Properties," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 115-135, July.
    11. Zhenyu Ming & Liping Zhang & Liqun Qi, 2020. "Expected residual minimization method for monotone stochastic tensor complementarity problem," Computational Optimization and Applications, Springer, vol. 77(3), pages 871-896, December.
    12. J. Burke & S. Xu, 2002. "Complexity of a Noninterior Path-Following Method for the Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 53-76, January.
    13. B. Chen, 2001. "Error Bounds for R0-Type and Monotone Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 108(2), pages 297-316, February.
    14. Zhang, Chao & Chen, Xiaojun & Sumalee, Agachai, 2011. "Robust Wardrop's user equilibrium assignment under stochastic demand and supply: Expected residual minimization approach," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 534-552, March.
    15. N. H. Xiu & J. Z. Zhang, 2002. "Global Projection-Type Error Bounds for General Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 213-228, January.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:joptap:v:150:y:2011:i:1:d:10.1007_s10957-011-9821-7. 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.