IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v56y2013i2p713-725.html
   My bibliography  Save this article

Generic uniqueness theorems with some applications

Author

Listed:
  • Dingtao Peng
  • Jian Yu
  • Naihua Xiu

Abstract

We first present a proper condition under which the image of a set-valued mapping becomes a singleton and then obtain several generic uniqueness theorems which can be applied to study the uniqueness of the solutions for nonlinear problems. As applications, we prove that, in the sense of Baire category, most optimization problems (respectively, saddle point problems and variational inequality problems) have unique solution. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Dingtao Peng & Jian Yu & Naihua Xiu, 2013. "Generic uniqueness theorems with some applications," Journal of Global Optimization, Springer, vol. 56(2), pages 713-725, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:713-725
    DOI: 10.1007/s10898-012-9903-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-9903-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-9903-6?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. Alexander J. Zaslavski, 2010. "Optimization on Metric and Normed Spaces," Springer Optimization and Its Applications, Springer, number 978-0-387-88621-3, June.
    2. Monica Bianchi & Siegfried Schaible, 2004. "Equilibrium Problems under Generalized Convexity and Generalized Monotonicity," Journal of Global Optimization, Springer, vol. 30(2), pages 121-134, 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. L. Q. Anh & P. Q. Khanh, 2007. "On the Stability of the Solution Sets of General Multivalued Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 271-284, November.
    2. Ayed E. Hashoosh & Mohsen Alimohammady & M. K. Kalleji, 2016. "Existence Results for Some Equilibrium Problems Involving -Monotone Bifunction," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-5, February.
    3. N. X. Hai & P. Q. Khanh, 2007. "Systems of Set-Valued Quasivariational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 55-67, October.
    4. Pham Ngoc Anh & Qamrul Hasan Ansari, 2021. "Auxiliary Principle Technique for Hierarchical Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 882-912, March.
    5. A. J. Zaslavski, 2014. "An Approximate Exact Penalty in Constrained Vector Optimization on Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 649-664, August.
    6. D. T. Peng & J. Yu & N. H. Xiu, 2012. "Generic Uniqueness of Solutions for a Class of Vector Ky Fan Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 165-179, October.
    7. Y. Jiang & S. Deng, 2014. "Enhanced Efficiency in Multi-objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 577-588, August.
    8. Enrico Biffis & Erik Chavez, 2017. "Satellite Data and Machine Learning for Weather Risk Management and Food Security," Risk Analysis, John Wiley & Sons, vol. 37(8), pages 1508-1521, August.
    9. Farajzadeh, A.P. & Plubtieng, S. & Ungchittrakool, K. & Kumtaeng, D., 2015. "Generalized mixed equilibrium problems with generalized α -η -monotone bifunction in topological vector spaces," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 313-319.
    10. P. Q. Khanh & L. T. Tung, 2012. "Local Uniqueness of Solutions to Ky Fan Vector Inequalities using Approximations as Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 840-854, December.

    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:jglopt:v:56:y:2013:i:2:p:713-725. 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.