IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v107y2000i3d10.1023_a1026495115191.html
   My bibliography  Save this article

System of Vector Equilibrium Problems and Its Applications

Author

Listed:
  • Q. H. Ansari

    (Aligarh Muslim University)

  • S. Schaible

    (University of California)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

In this paper, we introduce a system of vector equilibrium problems andprove the existence of a solution. As an application, we derive someexistence results for the system of vector variational inequalities. We alsoestablish some existence results for the system of vector optimizationproblems, which includes the Nash equilibrium problem as a special case.

Suggested Citation

  • Q. H. Ansari & S. Schaible & J. C. Yao, 2000. "System of Vector Equilibrium Problems and Its Applications," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 547-557, December.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:3:d:10.1023_a:1026495115191
    DOI: 10.1023/A:1026495115191
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1026495115191
    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:1026495115191?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. N. Hadjisavvas & S. Schaible, 1998. "From Scalar to Vector Equilibrium Problems in the Quasimonotone Case," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 297-309, February.
    2. Yu, Jian, 1999. "Essential equilibria of n-person noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 361-372, April.
    3. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
    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. Elena Molho & Domenico Scopelliti, 2023. "On the study of multistage stochastic vector quasi-variational problems," Journal of Global Optimization, Springer, vol. 86(4), pages 931-952, August.
    2. Ali Farajzadeh & Byung Soo Lee & Somyot Plubteing, 2016. "On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 584-599, February.
    3. L. J. Lin & Y. H. Liu, 2006. "Existence Theorems for Systems of Generalized Vector Quasiequilibrium Problems and Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 463-477, September.
    4. Q. H. Ansari & L. J. Lin & L. B. Su, 2005. "Systems of Simultaneous Generalized Vector Quasiequilibrium Problems and their Applications," Journal of Optimization Theory and Applications, Springer, vol. 127(1), pages 27-44, October.
    5. Csaba Farkas & Andrea Éva Molnár, 2013. "A Generalized Variational Principle and Its Application to Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 213-231, February.
    6. Jia-Wei Chen & Zhongping Wan & Yeol Cho, 2013. "Levitin–Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 33-64, February.
    7. N. J. Huang & J. Li & J. C. Yao, 2007. "Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 201-212, May.
    8. 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.
    9. Suhel Ahmad Khan, 2014. "System of Operator Quasi Equilibrium Problems," International Journal of Analysis, Hindawi, vol. 2014, pages 1-6, June.

    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. Ouayl Chadli & Qamrul Hasan Ansari & Suliman Al-Homidan, 2017. "Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 726-758, March.
    2. N. J. Huang & J. Li & J. C. Yao, 2007. "Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 201-212, May.
    3. I. V. Konnov & S. Schaible, 2000. "Duality for Equilibrium Problems under Generalized Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 395-408, February.
    4. Y.-P. Fang & N.-J. Huang, 2007. "Equivalence of Equilibrium Problems and Least Element Problems," Journal of Optimization Theory and Applications, Springer, vol. 132(3), pages 411-422, March.
    5. Lai-Jiu Lin & Qamrul Ansari & Yu-Jen Huang, 2007. "Some existence results for solutions of generalized vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 85-98, February.
    6. Q. H. Ansari & I. V. Konnov & J. C. Yao, 2001. "Existence of a Solution and Variational Principles for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 481-492, September.
    7. M. Fakhar & J. Zafarani, 2008. "Generalized Symmetric Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 397-409, March.
    8. 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.
    9. Jian-Wen Peng & Soon-Yi Wu & Yan Wang, 2012. "Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems with functional constraints," Journal of Global Optimization, Springer, vol. 52(4), pages 779-795, April.
    10. R. Hu & Y. P. Fang, 2009. "Feasibility-Solvability Theorem for a Generalized System," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 493-499, September.
    11. Mircea Balaj, 2022. "Scalar and vector equilibrium problems with pairs of bifunctions," Journal of Global Optimization, Springer, vol. 84(3), pages 739-753, November.
    12. Gábor Kassay & Mihaela Miholca, 2015. "Existence results for vector equilibrium problems given by a sum of two functions," Journal of Global Optimization, Springer, vol. 63(1), pages 195-211, September.
    13. F. Flores-Bazán & C. Vera, 2006. "Characterization of the Nonemptiness and Compactness of Solution Sets in Convex and Nonconvex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 185-207, August.
    14. L.J. Lin & Q.H. Ansari & J.Y. Wu, 2003. "Geometric Properties and Coincidence Theorems with Applications to Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 121-137, April.
    15. Q.H. Ansari & I.V. Konnov & J.C. Yao, 2002. "Characterizations of Solutions for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 435-447, June.
    16. Tran Van Su, 2018. "New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces," 4OR, Springer, vol. 16(2), pages 173-198, June.
    17. Yu Han, 2018. "Lipschitz Continuity of Approximate Solution Mappings to Parametric Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 763-793, September.
    18. César Gutiérrez & Rubén López, 2020. "On the Existence of Weak Efficient Solutions of Nonconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 880-902, June.
    19. Messaoud Deghdak & Monique Florenzano, 2011. "On The Existence Of Berge'S Strong Equilibrium," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 325-340.
    20. Junyi Fu & Sanhua Wang, 2013. "Generalized strong vector quasi-equilibrium problem with domination structure," Journal of Global Optimization, Springer, vol. 55(4), pages 839-847, 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:107:y:2000:i:3:d:10.1023_a:1026495115191. 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.