IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v102y1999i2d10.1023_a1021788625806.html
   My bibliography  Save this article

On Minimizing and Stationary Sequences of a New Class of Merit Functions for Nonlinear Complementarity Problems

Author

Listed:
  • H. D. Qi

Abstract

Motivated by the work of Fukushima and Pang (Ref. 1), we study the equivalent relationship between minimizing and stationary sequences of a new class of merit functions for nonlinear complementarity problems (NCP). These merit functions generalize that obtained via the squared Fischer–Burmeister NCP function, which was used in Ref. 1. We show that a stationary sequence {xk} ⊂ /Ren is a minimizing sequence under the condition that the function value sequence {F(x k)} is bounded above or the Jacobian matrix sequence {F′(x k)} is bounded, where F is the function involved in NCP. The latter condition is also assumed by Fukushima and Pang. The converse is true under the assumption of {F′(x k)} bounded. As an example shows, even for a bounded function F, the boundedness of the sequence {F′(x k)} is necessary for a minimizing sequence to be a stationary sequence.

Suggested Citation

  • H. D. Qi, 1999. "On Minimizing and Stationary Sequences of a New Class of Merit Functions for Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 411-431, August.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:2:d:10.1023_a:1021788625806
    DOI: 10.1023/A:1021788625806
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1021788625806
    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:1021788625806?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. O. L. Mangasarian, 1993. "Mathematical Programming in Neural Networks," INFORMS Journal on Computing, INFORMS, vol. 5(4), pages 349-360, 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. Eva K. Lee & Richard J. Gallagher & David A. Patterson, 2003. "A Linear Programming Approach to Discriminant Analysis with a Reserved-Judgment Region," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 23-41, February.
    2. 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.
    3. M. V. Solodov & S. K. Zavriev, 1998. "Error Stability Properties of Generalized Gradient-Type Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 663-680, September.
    4. Zhengyu Ma & Hong Seo Ryoo, 2021. "Spherical Classification of Data, a New Rule-Based Learning Method," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 44-71, April.
    5. W. Nick Street, 2005. "Oblique Multicategory Decision Trees Using Nonlinear Programming," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 25-31, February.
    6. Giovanni Felici & Klaus Truemper, 2002. "A MINSAT Approach for Learning in Logic Domains," INFORMS Journal on Computing, INFORMS, vol. 14(1), pages 20-36, February.
    7. P. S. Bradley & Usama M. Fayyad & O. L. Mangasarian, 1999. "Mathematical Programming for Data Mining: Formulations and Challenges," INFORMS Journal on Computing, INFORMS, vol. 11(3), pages 217-238, August.
    8. Palocsay, Susan W. & Stevens, Scott P. & Brookshire, Robert G. & Sacco, William J. & Copes, Wayne S. & Buckman, Robert F. & Smith, J. Stanley, 1996. "Using neural networks for trauma outcome evaluation," European Journal of Operational Research, Elsevier, vol. 93(2), pages 369-386, September.
    9. Sexton, Randall S. & Dorsey, Robert E. & Johnson, John D., 1999. "Optimization of neural networks: A comparative analysis of the genetic algorithm and simulated annealing," European Journal of Operational Research, Elsevier, vol. 114(3), pages 589-601, May.
    10. Orsenigo, Carlotta & Vercellis, Carlo, 2004. "Discrete support vector decision trees via tabu search," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 311-322, September.
    11. Thomas, Lyn C., 2000. "A survey of credit and behavioural scoring: forecasting financial risk of lending to consumers," International Journal of Forecasting, Elsevier, vol. 16(2), pages 149-172.

    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:102:y:1999:i:2:d:10.1023_a:1021788625806. 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.