IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v156y2013i2d10.1007_s10957-012-0123-5.html
   My bibliography  Save this article

Duality and a Characterization of Pseudoinvexity for Pareto and Weak Pareto Solutions in Nondifferentiable Multiobjective Programming

Author

Listed:
  • M. Arana-Jiménez

    (Universidad de Cádiz)

  • G. Ruiz-Garzón

    (Universidad de Cádiz)

  • R. Osuna-Gómez

    (Universidad de Sevilla)

  • B. Hernández-Jiménez

    (Universidad Pablo de Olavide)

Abstract

In this paper, we unify recent optimality results under directional derivatives by the introduction of new pseudoinvex classes of functions, in relation to the study of Pareto and weak Pareto solutions for nondifferentiable multiobjective programming problems. We prove that in order for feasible solutions satisfying Fritz John conditions to be Pareto or weak Pareto solutions, it is necessary and sufficient that the nondifferentiable multiobjective problem functions belong to these classes of functions, which is illustrated by an example. We also study the dual problem and establish weak, strong, and converse duality results.

Suggested Citation

  • M. Arana-Jiménez & G. Ruiz-Garzón & R. Osuna-Gómez & B. Hernández-Jiménez, 2013. "Duality and a Characterization of Pseudoinvexity for Pareto and Weak Pareto Solutions in Nondifferentiable Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 266-277, February.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:2:d:10.1007_s10957-012-0123-5
    DOI: 10.1007/s10957-012-0123-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-012-0123-5
    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/s10957-012-0123-5?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. Suneja, S.K. & Khurana, Seema & Vani, 2008. "Generalized nonsmooth invexity over cones in vector optimization," European Journal of Operational Research, Elsevier, vol. 186(1), pages 28-40, April.
    2. Antczak, Tadeusz, 2002. "Multiobjective programming under d-invexity," European Journal of Operational Research, Elsevier, vol. 137(1), pages 28-36, February.
    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. Slimani, Hachem & Radjef, Mohammed Said, 2010. "Nondifferentiable multiobjective programming under generalized dI-invexity," European Journal of Operational Research, Elsevier, vol. 202(1), pages 32-41, April.
    2. Tadeusz Antczak, 2023. "On directionally differentiable multiobjective programming problems with vanishing constraints," Annals of Operations Research, Springer, vol. 328(2), pages 1181-1212, September.
    3. Hachem Slimani & Mohammed-Said Radjef, 2016. "Generalized Fritz John optimality in nonlinear programming in the presence of equality and inequality constraints," Operational Research, Springer, vol. 16(2), pages 349-364, July.
    4. Li Tang & Ke Zhao, 2013. "Optimality conditions for a class of composite multiobjective nonsmooth optimization problems," Journal of Global Optimization, Springer, vol. 57(2), pages 399-414, October.
    5. Mishra, S. K. & Wang, S. Y. & Lai, K. K., 2005. "Nondifferentiable multiobjective programming under generalized d-univexity," European Journal of Operational Research, Elsevier, vol. 160(1), pages 218-226, January.
    6. Jiawei Chen & Elisabeth Köbis & Jen-Chih Yao, 2019. "Optimality Conditions and Duality for Robust Nonsmooth Multiobjective Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 411-436, 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:156:y:2013:i:2:d:10.1007_s10957-012-0123-5. 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.