IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v117y2003i1d10.1023_a1023648305969.html
   My bibliography  Save this article

Predictor-Corrector Smoothing Newton Method, Based on a New Smoothing Function, for Solving the Nonlinear Complementarity Problem with a P 0 Function

Author

Listed:
  • Z.H. Huang

    (Institute of Applied Mathematics)

  • J. Han

    (Institute of Applied Mathematics)

  • Z. Chen

    (Suzhou University)

Abstract

By smoothing a perturbed minimum function, we propose in this paper a new smoothing function. The existence and continuity of a smooth path for solving the nonlinear complementarity problem (NCP) with a P 0 function are discussed. We investigate the boundedness of the iteration sequence generated by noninterior continuation/smoothing methods under the assumption that the solution set of the NCP is nonempty and bounded. Based on the new smoothing function, we present a predictor-corrector smoothing Newton algorithm for solving the NCP with a P 0 function, which is shown to be globally linearly and locally superlinearly convergent under suitable assumptions. Some preliminary computational results are reported.

Suggested Citation

  • Z.H. Huang & J. Han & Z. Chen, 2003. "Predictor-Corrector Smoothing Newton Method, Based on a New Smoothing Function, for Solving the Nonlinear Complementarity Problem with a P 0 Function," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 39-68, April.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:1:d:10.1023_a:1023648305969
    DOI: 10.1023/A:1023648305969
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1023648305969
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1023648305969?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. James V. Burke & Song Xu, 1998. "The Global Linear Convergence of a Noninterior Path-Following Algorithm for Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 719-734, August.
    2. Masakazu Kojima & Nimrod Megiddo & Toshihito Noma, 1991. "Homotopy Continuation Methods for Nonlinear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 16(4), pages 754-774, November.
    3. M. Seetharama Gowda & Roman Sznajder, 1999. "Weak Univalence and Connectedness of Inverse Images of Continuous Functions," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 255-261, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tang, Jingyong & Zhou, Jinchuan & Fang, Liang, 2015. "A non-monotone regularization Newton method for the second-order cone complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 743-756.
    2. Changfeng Ma, 2010. "A new smoothing and regularization Newton method for P 0 -NCP," Journal of Global Optimization, Springer, vol. 48(2), pages 241-261, October.
    3. Jingyong Tang & Jinchuan Zhou, 2021. "Quadratic convergence analysis of a nonmonotone Levenberg–Marquardt type method for the weighted nonlinear complementarity problem," Computational Optimization and Applications, Springer, vol. 80(1), pages 213-244, September.
    4. Bilian Chen & Changfeng Ma, 2011. "A new smoothing Broyden-like method for solving nonlinear complementarity problem with a P 0 -function," Journal of Global Optimization, Springer, vol. 51(3), pages 473-495, November.
    5. Liqun Qi & Zheng-Hai Huang, 2019. "Tensor Complementarity Problems—Part II: Solution Methods," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 365-385, November.

    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. Yun-Bin Zhao & Duan Li, 2001. "On a New Homotopy Continuation Trajectory for Nonlinear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 119-146, February.
    2. L. Qi & D. Sun, 2002. "Smoothing Functions and Smoothing Newton Method for Complementarity and Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 121-147, April.
    3. Y. B. Zhao & D. Li, 2000. "Strict Feasibility Conditions in Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 641-664, December.
    4. Zhao, Na, 2015. "Finite termination of a Newton-type algorithm based on a new class of smoothing functions for the affine variational inequality problem," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 926-934.
    5. 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.
    6. Bilian Chen & Changfeng Ma, 2011. "A new smoothing Broyden-like method for solving nonlinear complementarity problem with a P 0 -function," Journal of Global Optimization, Springer, vol. 51(3), pages 473-495, November.
    7. Wang Qinggang & Zhao Jinling & Yang Qingzhi, 2010. "Some non-interior path-following methods based on a scaled central path for linear complementarity problems," Computational Optimization and Applications, Springer, vol. 46(1), pages 31-49, May.
    8. B. Chen & N. Xiu, 2001. "Superlinear Noninterior One-Step Continuation Method for Monotone LCP in the Absence of Strict Complementarity," Journal of Optimization Theory and Applications, Springer, vol. 108(2), pages 317-332, February.
    9. Defeng Sun & Jie Sun, 2002. "Semismooth Matrix-Valued Functions," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 150-169, February.
    10. Liqun Qi & Zheng-Hai Huang, 2019. "Tensor Complementarity Problems—Part II: Solution Methods," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 365-385, November.
    11. Birbil, S.I. & Fang, S-C. & Han, J., 2002. "On the Finite Termination of An Entropy Function Based Smoothing Newton Method for Vertical Linear Complementarity Problems," ERIM Report Series Research in Management ERS-2002-72-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    12. Fang, S-C. & Han, J. & Huang, Z. & Birbil, S.I., 2002. "On the finite termination of an entropy function based smoothing Newton method for vertical linear complementarity problems," Econometric Institute Research Papers EI 2002-50, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. Lixing Han, 2019. "A Continuation Method for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 949-963, March.
    14. Wei Liu & Chan He, 2018. "Equilibrium Conditions of a Logistics Service Supply Chain with a New Smoothing Algorithm," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(02), pages 1-22, April.
    15. Changfeng Ma, 2010. "A new smoothing and regularization Newton method for P 0 -NCP," Journal of Global Optimization, Springer, vol. 48(2), pages 241-261, 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:joptap:v:117:y:2003:i:1:d:10.1023_a:1023648305969. 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.