IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v52y2012i3p805-824.html
   My bibliography  Save this article

Properties and construction of NCP functions

Author

Listed:
  • Aurél Galántai

Abstract

The nonlinear complementarity or NCP functions were introduced by Mangasarian and these functions are proved to be useful in constrained optimization and elsewhere. Interestingly enough there are only two general methods to derive such functions, while the known or used NCP functions are either individual constructions or modifications of the few individual NCP functions such as the Fischer-Burmeister function. In the paper we analyze the elementary properties of NCP functions and the various techniques used to obtain such functions from old ones. We also prove some new nonexistence results on the possible forms of NCP functions. Then we develop and analyze several new methods for the construction of nonlinear complementarity functions that are based on various geometric arguments or monotone transformations. The appendix of the paper contains the list and source of the known NCP functions. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Aurél Galántai, 2012. "Properties and construction of NCP functions," Computational Optimization and Applications, Springer, vol. 52(3), pages 805-824, July.
    • Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:805-824
    DOI: 10.1007/s10589-011-9428-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-011-9428-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-011-9428-9?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. 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.
    2. X. Chen & L. Qi & Y. F. Yang, 2002. "Lagrangian Globalization Methods for Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 77-95, January.
    3. N. Yamashita, 1998. "Properties of Restricted NCP Functions for Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 701-717, September.
    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. Johanna Burtscheidt & Matthias Claus, 2017. "A Note on Stability for Risk-Averse Stochastic Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 298-308, January.

    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. S. Mohsen Miri & Sohrab Effati, 2015. "On Generalized Convexity of Nonlinear Complementarity Functions," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 723-730, February.
    2. Azam Asanjarani, 2023. "A Finsler Geometrical Programming Approach to the Nonlinear Complementarity Problem of Traffic Equilibrium," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 797-809, March.
    3. Liyan Xu & Bo Yu, 2014. "CVaR-constrained stochastic programming reformulation for stochastic nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 58(2), pages 483-501, June.
    4. S. H. Pan & J.-S. Chen, 2009. "Growth Behavior of Two Classes of Merit Functions for Symmetric Cone Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 167-191, April.
    5. Boshi Tian & Yaohua Hu & Xiaoqi Yang, 2015. "A box-constrained differentiable penalty method for nonlinear complementarity problems," Journal of Global Optimization, Springer, vol. 62(4), pages 729-747, August.
    6. Patrick Mehlitz, 2020. "A comparison of solution approaches for the numerical treatment of or-constrained optimization problems," Computational Optimization and Applications, Springer, vol. 76(1), pages 233-275, May.
    7. J.-S. Chen & Z.-H. Huang & C.-Y. She, 2011. "A new class of penalized NCP-functions and its properties," Computational Optimization and Applications, Springer, vol. 50(1), pages 49-73, September.
    8. J. M. Peng, 1998. "Derivative-Free Methods for Monotone Variational Inequality and Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 235-252, October.
    9. 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.
    10. N. Yamashita, 1998. "Properties of Restricted NCP Functions for Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 701-717, September.
    11. Xiaojun Chen & Masao Fukushima, 2005. "Expected Residual Minimization Method for Stochastic Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1022-1038, November.
    12. Gaoxi Li & Xinmin Yang, 2021. "Convexification Method for Bilevel Programs with a Nonconvex Follower’s Problem," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 724-743, March.
    13. Samir Adly & Hadia Rammal, 2013. "A new method for solving Pareto eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 55(3), pages 703-731, July.

    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:52:y:2012:i:3:p:805-824. 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.