IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v106y2000i3d10.1023_a1004697127040.html
   My bibliography  Save this article

On Nondifferentiable and Nonconvex Vector Optimization Problems

Author

Listed:
  • Q. H. Ansari

    (Aligarh Muslim University)

  • J> C> Yao

    (National Sun Yat-sen University)

Abstract

In this paper, we prove the equivalence among the Minty vector variational-like inequality, Stampacchia vector variational-like inequality, and a nondifferentiable and nonconvex vector optimization problem. By using a fixed-point theorem, we establish also an existence theorem for generalized weakly efficient solutions to the vector optimization problem for nondifferentiable and nonconvex functions.

Suggested Citation

  • Q. H. Ansari & J> C> Yao, 2000. "On Nondifferentiable and Nonconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 475-488, September.
    • Handle: RePEc:spr:joptap:v:106:y:2000:i:3:d:10.1023_a:1004697127040
    DOI: 10.1023/A:1004697127040
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1004697127040
    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:1004697127040?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. K. L. Lin & D. P. Yang & J. C. Yao, 1997. "Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 117-125, January.
    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. X.Q. Yang & J.C. Yao, 2002. "Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 407-417, November.
    2. T. Jabarootian & J. Zafarani, 2008. "Generalized Vector Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 15-30, January.
    3. S. Al-Homidan & Q. H. Ansari & S. Schaible, 2007. "Existence of Solutions of Systems of Generalized Implicit Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 515-531, September.
    4. Q. H. Ansari & G. M. Lee, 2010. "Nonsmooth Vector Optimization Problems and Minty Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 1-16, April.
    5. S. K. Mishra & S. Y. Wang & K. K. Lai, 2008. "Gap Function for Set-Valued Vector Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 77-84, July.
    6. S. Al-Homidan & Q. H. Ansari, 2010. "Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 1-11, 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. Ren-you Zhong & Zhen Dou & Jiang-hua Fan, 2015. "Degree Theory and Solution Existence of Set-Valued Vector Variational Inequalities in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 527-549, November.
    2. Y. P. Fang & N. J. Huang, 2006. "Feasibility and Solvability for Vector Complementarity Problems1," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 373-390, June.
    3. G. Y. Chen & X. Q. Yang, 2002. "Characterizations of Variable Domination Structures via Nonlinear Scalarization," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 97-110, January.
    4. 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.
    5. S.J. Li & G.Y. Chen & K.L. Teo, 2002. "On the Stability of Generalized Vector Quasivariational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(2), pages 283-295, May.
    6. X. H. Gong, 2008. "Continuity of the Solution Set to Parametric Weak Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 35-46, October.
    7. J. Li & G. Mastroeni, 2010. "Vector Variational Inequalities Involving Set-valued Mappings via Scalarization with Applications to Error Bounds for Gap Functions," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 355-372, May.
    8. O. Chadli & S. Schaible & J. C. Yao, 2004. "Regularized Equilibrium Problems with Application to Noncoercive Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 571-596, June.
    9. Jiawei Chen & Shengjie Li & Zhongping Wan & Jen-Chih Yao, 2015. "Vector Variational-Like Inequalities with Constraints: Separation and Alternative," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 460-479, August.
    10. X. H. Gong, 2001. "Efficiency and Henig Efficiency for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 139-154, January.
    11. Szilárd László & Adrian Viorel, 2015. "Densely Defined Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 52-75, July.
    12. O. Chadli & Z. Liu & J. C. Yao, 2007. "Applications of Equilibrium Problems to a Class of Noncoercive Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 89-110, January.
    13. Tadeusz Antczak & Najeeb Abdulaleem, 2024. "On vector variational E-inequalities and differentiable vector optimization problem," OPSEARCH, Springer;Operational Research Society of India, vol. 61(1), pages 460-482, March.
    14. Q. H. Ansari & T. C. Lai & J. C. Yao, 1999. "On the Equivalence of Extended Generalized Complementarity and Generalized Least-Element Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 277-288, August.
    15. S. K. Mishra & S. Y. Wang & K. K. Lai, 2008. "Gap Function for Set-Valued Vector Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 77-84, July.
    16. M.H. Kim & S.H. Kum & G.M. Lee, 2002. "Vector Variational Inequalities Involving Vector Maximal Points," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 593-607, September.
    17. Y. C. Lin, 2009. "On F-Implicit Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 557-568, September.
    18. Y. Chiang & J. C. Yao, 2004. "Vector Variational Inequalities and the (S)+ Condition," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 271-290, November.
    19. Y.P. Fang & N.J. Huang, 2003. "Variational-Like Inequalities with Generalized Monotone Mappings in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 327-338, August.
    20. S. Kum & W. K. Kim, 2007. "Applications of Generalized Variational and Quasivariational Inequalities with Operator Solutions in a TVS," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 65-75, 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:106:y:2000:i:3:d:10.1023_a:1004697127040. 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.