IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v80y2021i1d10.1007_s10898-021-01018-x.html
   My bibliography  Save this article

Duality in nonconvex vector optimization

Author

Listed:
  • Refail Kasimbeyli

    (Eskisehir Technical University)

  • Masoud Karimi

    (Mehrgan Niro Pouya Company)

Abstract

In this paper, duality relations in nonconvex vector optimization are studied. An augmented Lagrangian function associated with the primal problem is introduced and efficient solutions to the given vector optimization problem, are characterized in terms of saddle points of this Lagrangian. The dual problem to the given primal one, is constructed with the help of the augmented Lagrangian introduced and weak and strong duality theorems are proved. Illustrative examples for duality relations are provided.

Suggested Citation

  • Refail Kasimbeyli & Masoud Karimi, 2021. "Duality in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 139-160, May.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:1:d:10.1007_s10898-021-01018-x
    DOI: 10.1007/s10898-021-01018-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-021-01018-x
    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/s10898-021-01018-x?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. Nergiz Kasimbeyli, 2015. "Existence and characterization theorems in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 62(1), pages 155-165, May.
    2. Shokouh Shahbeyk & Majid Soleimani-damaneh & Refail Kasimbeyli, 2018. "Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure," Journal of Global Optimization, Springer, vol. 71(2), pages 383-405, June.
    3. Radu Boţ & Sorin-Mihai Grad & Gert Wanka, 2007. "A general approach for studying duality in multiobjective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 417-444, June.
    4. Abbas Sayadi-bander & Latif Pourkarimi & Refail Kasimbeyli & Hadi Basirzadeh, 2017. "Coradiant sets and $$\varepsilon $$ ε -efficiency in multiobjective optimization," Journal of Global Optimization, Springer, vol. 68(3), pages 587-600, July.
    5. A. Y. Azimov, 2008. "Duality for Set-Valued Multiobjective Optimization Problems, Part 1: Mathematical Programming," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 61-74, April.
    6. Gasimov, Rafail N. & Sipahioglu, Aydin & Sarac, Tugba, 2007. "A multi-objective programming approach to 1.5-dimensional assortment problem," European Journal of Operational Research, Elsevier, vol. 179(1), pages 64-79, May.
    7. Refail Kasimbeyli, 2013. "A conic scalarization method in multi-objective optimization," Journal of Global Optimization, Springer, vol. 56(2), pages 279-297, June.
    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. Nergiz Kasimbeyli, 2015. "Existence and characterization theorems in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 62(1), pages 155-165, May.
    2. Derya Deliktaş, 2022. "Self-adaptive memetic algorithms for multi-objective single machine learning-effect scheduling problems with release times," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 748-784, September.
    3. Nguyen Dinh & Dang Hai Long, 2022. "A Perturbation Approach to Vector Optimization Problems: Lagrange and Fenchel–Lagrange Duality," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 713-748, August.
    4. Gabriele Eichfelder & Refail Kasimbeyli, 2014. "Properly optimal elements in vector optimization with variable ordering structures," Journal of Global Optimization, Springer, vol. 60(4), pages 689-712, December.
    5. Sierra-Paradinas, María & Soto-Sánchez, Óscar & Alonso-Ayuso, Antonio & Martín-Campo, F. Javier & Gallego, Micael, 2021. "An exact model for a slitting problem in the steel industry," European Journal of Operational Research, Elsevier, vol. 295(1), pages 336-347.
    6. Brian Dandurand & Margaret M. Wiecek, 2016. "Quadratic scalarization for decomposed multiobjective optimization," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 1071-1096, October.
    7. Refail Kasimbeyli, 2013. "A conic scalarization method in multi-objective optimization," Journal of Global Optimization, Springer, vol. 56(2), pages 279-297, June.
    8. Zhiang Zhou & Wenbin Wei & Fei Huang & Kequan Zhao, 2024. "Approximate weak efficiency of the set-valued optimization problem with variable ordering structures," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-13, October.
    9. Behnam Soleimani, 2014. "Characterization of Approximate Solutions of Vector Optimization Problems with a Variable Order Structure," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 605-632, August.
    10. Abbas Sayadi-bander & Latif Pourkarimi & Refail Kasimbeyli & Hadi Basirzadeh, 2017. "Coradiant sets and $$\varepsilon $$ ε -efficiency in multiobjective optimization," Journal of Global Optimization, Springer, vol. 68(3), pages 587-600, July.
    11. Vahid Morovati & Hadi Basirzadeh & Latif Pourkarimi, 2018. "Quasi-Newton methods for multiobjective optimization problems," 4OR, Springer, vol. 16(3), pages 261-294, September.
    12. Shokouh Shahbeyk & Majid Soleimani-damaneh & Refail Kasimbeyli, 2018. "Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure," Journal of Global Optimization, Springer, vol. 71(2), pages 383-405, June.

    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:jglopt:v:80:y:2021:i:1:d:10.1007_s10898-021-01018-x. 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.