IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v102y1999i2d10.1023_a1021724306242.html
   My bibliography  Save this article

On the Equivalence of Extended Generalized Complementarity and Generalized Least-Element Problems

Author

Listed:
  • Q. H. Ansari

    (Aligarh Muslim University
    National Sun Yat-sen University)

  • T. C. Lai

    (National Taiwan University)

  • J. C. Yao

    (National Sun Yat-sen University)

Abstract

In this paper, we derive some equivalences of generalized nonlinear programs, generalized least-element problems, and extended generalized complementarity problems under certain regularity and growth conditions. We also generalize the notion of a Z-map for point-to-set maps. Our results extend recent results by Schaible and Yao (Ref. 1).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:2:d:10.1023_a:1021724306242
    DOI: 10.1023/A:1021724306242
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1021724306242
    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:1021724306242?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. Romesh Saigal, 1976. "Extension of the Generalized Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 260-266, August.
    2. 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.
    3. R. C. Riddell, 1981. "Equivalence of Nonlinear Complementarity Problems and Least Element Problems in Banach Lattices," Mathematics of Operations Research, INFORMS, vol. 6(3), pages 462-474, August.
    4. Richard W. Cottle & Jong-Shi Pang, 1978. "A Least-Element Theory of Solving Linear Complementarity Problems as Linear Programs," Mathematics of Operations Research, INFORMS, vol. 3(2), pages 155-170, May.
    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. E. Allevi & A. Gnudi & S. Schaible & M. Vespucci, 2010. "Equilibrium and least element problems for multivalued functions," Journal of Global Optimization, Springer, vol. 46(4), pages 561-569, April.
    2. Huang, N.J. & Yang, X.Q. & Chan, W.K., 2007. "Vector complementarity problems with a variable ordering relation," European Journal of Operational Research, Elsevier, vol. 176(1), pages 15-26, January.
    3. F. Giannessi & G. Mastroeni & X. Yang, 2012. "Survey on Vector Complementarity Problems," Journal of Global Optimization, Springer, vol. 53(1), pages 53-67, May.
    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.

    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. O. Chaldi & Z. Chbani & H. Riahi, 2000. "Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 105(2), pages 299-323, May.
    2. 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.
    3. 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.
    4. B. Djafari Rouhani & B. Ahmadi Kakavandi, 2006. "Infinite Time-Dependent Network Equilibria with a Multivalued Cost Function," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 405-415, December.
    5. X. P. Ding, 1997. "Generalized Variational-Like Inequalities with Nonmonotone Set-Valued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 601-613, December.
    6. 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.
    7. Massimo Marinacci & Luigi Montrucchio, 2017. "Unique Tarski Fixed Points," Working Papers 604, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    8. 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.
    9. Sonia & Ratna Dev Sarma, 2023. "A topological approach for vector quasi-variational inequalities with set-valued functions," Computational Management Science, Springer, vol. 20(1), pages 1-13, December.
    10. 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.
    11. 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.
    12. Massimo Marinacci & Luigi Montrucchio, 2019. "Unique Tarski Fixed Points," Management Science, INFORMS, vol. 44(4), pages 1174-1191, November.
    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. S. Park, 1997. "Generalized Equilibrium Problems and Generalized Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 409-417, November.
    15. 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.
    16. 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.
    17. 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.
    18. Paolo Cubiotti & Jen-Chih Yao, 1997. "Discontinuous implicit quasi-variational inequalities with applications to fuzzy mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 213-228, June.
    19. 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.
    20. X. H. Gong, 2007. "Connectedness of the Solution Sets and Scalarization for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 151-161, May.

    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:1021724306242. 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.