IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v134y2007i1d10.1007_s10957-007-9237-6.html
   My bibliography  Save this article

Lagrangian Duality in Set-Valued Optimization

Author

Listed:
  • E. Hernández

    (Universidad Nacional de Educación a Distancia)

  • L. Rodríguez-Marín

    (Universidad Nacional de Educación a Distancia)

Abstract

In this paper, we study optimization problems where the objective function and the binding constraints are set-valued maps and the solutions are defined by means of set-relations among all the images sets (Kuroiwa, D. in Takahashi, W., Tanaka, T. (eds.) Nonlinear analysis and convex analysis, pp. 221–228, 1999). We introduce a new dual problem, establish some duality theorems and obtain a Lagrangian multiplier rule of nonlinear type under convexity assumptions. A necessary condition and a sufficient condition for the existence of saddle points are given.

Suggested Citation

  • E. Hernández & L. Rodríguez-Marín, 2007. "Lagrangian Duality in Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 119-134, July.
    • Handle: RePEc:spr:joptap:v:134:y:2007:i:1:d:10.1007_s10957-007-9237-6
    DOI: 10.1007/s10957-007-9237-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9237-6
    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/s10957-007-9237-6?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. X. D. H. Truong, 1997. "Cones Admitting Strictly Positive Functionals and Scalarization of Some Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 355-372, May.
    2. P. H. Sach, 2003. "Nearly Subconvexlike Set-Valued Maps and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 335-356, 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. P. Q. Khanh & N. D. Tuan, 2008. "Higher-Order Variational Sets and Higher-Order Optimality Conditions for Proper Efficiency in Set-Valued Nonsmooth Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 243-261, November.
    2. Z. A. Zhou & X. M. Yang, 2011. "Optimality Conditions of Generalized Subconvexlike Set-Valued Optimization Problems Based on the Quasi-Relative Interior," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 327-340, August.
    3. P. H. Sach & D. S. Kim & L. A. Tuan & G. M. Lee, 2008. "Duality Results for Generalized Vector Variational Inequalities with Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 105-123, January.
    4. L. Y. Xia & J. H. Qiu, 2008. "Superefficiency in Vector Optimization with Nearly Subconvexlike Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 125-137, January.
    5. M. Ehrgott & S. Ruzika, 2008. "Improved ε-Constraint Method for Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 375-396, September.
    6. P. H. Sach, 2007. "Moreau–Rockafellar Theorems for Nonconvex Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 213-227, May.
    7. Zhiang Zhou & Wang Chen & Xinmin Yang, 2019. "Scalarizations and Optimality of Constrained Set-Valued Optimization Using Improvement Sets and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 944-962, 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:joptap:v:134:y:2007:i:1:d:10.1007_s10957-007-9237-6. 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.