IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v270y2015icp926-934.html
   My bibliography  Save this article

Finite termination of a Newton-type algorithm based on a new class of smoothing functions for the affine variational inequality problem

Author

Listed:
  • Zhao, Na

Abstract

In this paper, we propose a new class of smoothing functions. Some favorable properties of the functions are investigated. By using the proposed functions, the affine variational inequality problem (AVI) is reformulated as a system of parameterized smooth equations. A Newton method with a projection-type testing procedure is proposed to solve the equations. Under mild assumptions, we show that the algorithm may find a maximally complementary solution to the monotone AVI in a finite number of iterations. Preliminary numerical results indicate that the proposed smoothing functions are valuable.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:926-934
    DOI: 10.1016/j.amc.2015.08.045
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315011005
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.08.045?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. He, Bing-sheng & Yang, Hai & Zhang, Chen-song, 2004. "A modified augmented Lagrangian method for a class of monotone variational inequalities," European Journal of Operational Research, Elsevier, vol. 159(1), pages 35-51, 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. Defeng Sun & Jie Sun, 2002. "Semismooth Matrix-Valued Functions," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 150-169, February.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Meng, Qiang & Huang, Yikai & Cheu, Ruey Long, 2009. "Competitive facility location on decentralized supply chains," European Journal of Operational Research, Elsevier, vol. 196(2), pages 487-499, July.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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:eee:apmaco:v:270:y:2015:i:c:p:926-934. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.