IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v124y2005i1d10.1007_s10957-004-6466-9.html
   My bibliography  Save this article

Coercivity Conditions for Equilibrium Problems

Author

Listed:
  • M. Bianchi

    (Università Cattolica del Sacro Cuore)

  • R. Pini

    (Università di Milano- Bicocca)

Abstract

The study of the existence of solutions of equilibrium problems on unbounded domains involves usually the same sufficient assumptions as for bounded domains together with a coercivity condition. We focus on two different conditions: the first is obtained assuming the existence of a bounded set such that no elements outside is a candidate for a solution; the second allows the solution set to be unbounded. Our results exploit the generalized monotonicity properties of the function f defining the equilibrium problem. It turns out that, in both the pseudomonotone and the quasimonotone setting, an equivalence can be stated between the nonemptyness and boundedness of the solution set and these coercivity conditions. In the pseudomonotone case, we compare our coercivity conditions with various coercivity conditions that appeared in the literature.

Suggested Citation

  • M. Bianchi & R. Pini, 2005. "Coercivity Conditions for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 79-92, January.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:1:d:10.1007_s10957-004-6466-9
    DOI: 10.1007/s10957-004-6466-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-004-6466-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-004-6466-9?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. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    2. M. Bianchi & N. Hadjisavvas & S. Schaible, 2004. "Minimal Coercivity Conditions and Exceptional Families of Elements in Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 1-17, July.
    3. Y. B. Zhao & J. Y. Han & H. D. Qi, 1999. "Exceptional Families and Existence Theorems for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 475-495, May.
    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. Y. Chiang, 2010. "Variational inequalities on weakly compact sets," Journal of Global Optimization, Springer, vol. 46(3), pages 465-473, March.
    2. I. Konnov, 2014. "On penalty methods for non monotone equilibrium problems," Journal of Global Optimization, Springer, vol. 59(1), pages 131-138, May.
    3. J. H. Fan & X. G. Wang, 2009. "Solvability of Generalized Variational Inequality Problems for Unbounded Sets in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 59-74, October.
    4. I. Konnov & D. Dyabilkin, 2011. "Nonmonotone equilibrium problems: coercivity conditions and weak regularization," Journal of Global Optimization, Springer, vol. 49(4), pages 575-587, April.
    5. M. Castellani & M. Giuli, 2013. "Refinements of existence results for relaxed quasimonotone equilibrium problems," Journal of Global Optimization, Springer, vol. 57(4), pages 1213-1227, December.
    6. G. Isac & S. Z. Németh, 2008. "REFE-Acceptable Mappings: Necessary and Sufficient Condition for the Nonexistence of a Regular Exceptional Family of Elements," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 507-520, June.
    7. M. Bianchi & N. Hadjisavvas & S. Schaible, 2006. "Exceptional Families of Elements for Variational Inequalities in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 23-31, April.
    8. Nicuşor Costea & Daniel Alexandru Ion & Cezar Lupu, 2012. "Variational-Like Inequality Problems Involving Set-Valued Maps and Generalized Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 79-99, October.
    9. Ren-you Zhong & Nan-jing Huang, 2012. "Strict Feasibility for Generalized Mixed Variational Inequality in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 696-709, March.
    10. Yiran He, 2017. "Solvability of the Minty Variational Inequality," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 686-692, September.
    11. L.R. Huang & K. F. Ng, 2005. "Equivalent Optimization Formulations and Error Bounds for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 299-314, May.
    12. Yan, Weijie & Ling, Chen & Ling, Liyun & He, Hongjin, 2019. "Generalized tensor equations with leading structured tensors," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 311-324.
    13. Mircea Balaj, 2021. "Intersection theorems for generalized weak KKM set‐valued mappings with applications in optimization," Mathematische Nachrichten, Wiley Blackwell, vol. 294(7), pages 1262-1276, July.
    14. John Cotrina & Javier Zúñiga, 2019. "Quasi-equilibrium problems with non-self constraint map," Journal of Global Optimization, Springer, vol. 75(1), pages 177-197, September.
    15. Massimiliano Giuli, 2013. "Closedness of the Solution Map in Quasivariational Inequalities of Ky Fan Type," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 130-144, July.
    16. Z.H. Huang, 2003. "Generalization of an Existence Theorem for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 567-585, September.
    17. Somaye Jafari & Ali Farajzadeh & Sirous Moradi, 2016. "Locally Densely Defined Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 804-817, September.
    18. John Cotrina & Anton Svensson, 2021. "The finite intersection property for equilibrium problems," Journal of Global Optimization, Springer, vol. 79(4), pages 941-957, April.
    19. 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.
    20. Y. B. Zhao & G. Isac, 2000. "Quasi-P*-Maps, P(τ, α, β)-Maps, Exceptional Family of Elements, and Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 213-231, April.

    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:124:y:2005:i:1:d:10.1007_s10957-004-6466-9. 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.