IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v186y2020i3d10.1007_s10957-020-01732-8.html
   My bibliography  Save this article

Necessary Conditions for Nondominated Solutions in Vector Optimization

Author

Listed:
  • Truong Q. Bao

    (Northern Michigan University)

  • Lidia Huerga

    (UNED)

  • Bienvenido Jiménez

    (UNED)

  • Vicente Novo

    (UNED)

Abstract

In this paper, we study characterizations and necessary conditions for nondominated points of sets and nondominated solutions of vector-valued functions in vector optimization with variable domination structure. We study not only the case, where the intersection of all the involved domination sets has a nonzero element, but also the case, where it might be the singleton. While the first case has been studied earlier, the second case has not, to the best of our knowledge, done yet. Our results extend and improve the existing results in vector optimization with a fixed ordering cone and with a variable ordering structure.

Suggested Citation

  • Truong Q. Bao & Lidia Huerga & Bienvenido Jiménez & Vicente Novo, 2020. "Necessary Conditions for Nondominated Solutions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 826-842, September.
  • Handle: RePEc:spr:joptap:v:186:y:2020:i:3:d:10.1007_s10957-020-01732-8
    DOI: 10.1007/s10957-020-01732-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-020-01732-8
    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/s10957-020-01732-8?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. Adan, M. & Novo, V., 2003. "Weak efficiency in vector optimization using a closure of algebraic type under cone-convexlikeness," European Journal of Operational Research, Elsevier, vol. 149(3), pages 641-653, September.
    2. Truong Q. Bao & Boris S. Mordukhovich, 2014. "Necessary Nondomination Conditions in Set and Vector Optimization with Variable Ordering Structures," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 350-370, August.
    3. Gabriele Eichfelder, 2011. "Optimal Elements in Vector Optimization with a Variable Ordering Structure," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 217-240, November.
    4. Marius Durea & Radu Strugariu & Christiane Tammer, 2015. "On set-valued optimization problems with variable ordering structure," Journal of Global Optimization, Springer, vol. 61(4), pages 745-767, April.
    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. Elena-Andreea Florea, 2018. "Vector Optimization Problems with Generalized Functional Constraints in Variable Ordering Structure Setting," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 94-118, July.
    2. Ovidiu Bagdasar & Nicolae Popovici, 2018. "Unifying local–global type properties in vector optimization," Journal of Global Optimization, Springer, vol. 72(2), pages 155-179, October.
    3. 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.
    4. Gabriele Eichfelder & Maria Pilecka, 2016. "Set Approach for Set Optimization with Variable Ordering Structures Part II: Scalarization Approaches," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 947-963, December.
    5. Gabriele Eichfelder & Maria Pilecka, 2016. "Set Approach for Set Optimization with Variable Ordering Structures Part I: Set Relations and Relationship to Vector Approach," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 931-946, December.
    6. Bettina Zargini, 2022. "Multiobjective Location Problems with Variable Domination Structures and an Application to Select a New Hub Airport," Logistics, MDPI, vol. 6(2), pages 1-13, March.
    7. Marius Durea & Radu Strugariu & Christiane Tammer, 2017. "On Some Methods to Derive Necessary and Sufficient Optimality Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 738-763, December.
    8. C. Gutiérrez & L. Huerga & B. Jiménez & V. Novo, 2018. "Approximate solutions of vector optimization problems via improvement sets in real linear spaces," Journal of Global Optimization, Springer, vol. 70(4), pages 875-901, April.
    9. J. Y. Bello Cruz & G. Bouza Allende, 2014. "A Steepest Descent-Like Method for Variable Order Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 371-391, August.
    10. T. Q. Bao & B. S. Mordukhovich & A. Soubeyran, 2015. "Variational Analysis in Psychological Modeling," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 290-315, January.
    11. M. Adán & V. Novo, 2004. "Proper Efficiency in Vector Optimization on Real Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 515-540, June.
    12. M. Chinaie & F. Fakhar & M. Fakhar & H. R. Hajisharifi, 2019. "Weak minimal elements and weak minimal solutions of a nonconvex set-valued optimization problem," Journal of Global Optimization, Springer, vol. 75(1), pages 131-141, September.
    13. Z. A. Zhou & J. W. Peng, 2012. "Scalarization of Set-Valued Optimization Problems with Generalized Cone Subconvexlikeness in Real Ordered Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 830-841, September.
    14. Christian Günther & Bahareh Khazayel & Christiane Tammer, 2022. "Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 408-442, June.
    15. Truong Q. Bao & Boris S. Mordukhovich, 2014. "Necessary Nondomination Conditions in Set and Vector Optimization with Variable Ordering Structures," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 350-370, August.
    16. Zhi-Ang Zhou & Xin-Min Yang, 2014. "Scalarization of $$\epsilon $$ ϵ -Super Efficient Solutions of Set-Valued Optimization Problems in Real Ordered Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 680-693, August.
    17. Christian Sommer, 2014. "Geometrical and Topological Properties of a Parameterized Binary Relation in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 815-840, December.
    18. Elham Kiyani & Majid Soleimani-damaneh, 2014. "Algebraic Interior and Separation on Linear Vector Spaces: Some Comments," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 994-998, June.
    19. 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.
    20. Davide LA TORRE & Nicolae POPOVICI & Matteo ROCCA, 2008. "Scalar characterization of explicitly quasiconvex set-valued maps," Departmental Working Papers 2008-01, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

    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:186:y:2020:i:3:d:10.1007_s10957-020-01732-8. 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.