IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v178y2018i1d10.1007_s10957-018-1269-6.html
   My bibliography  Save this article

Vector Optimization Problems with Generalized Functional Constraints in Variable Ordering Structure Setting

Author

Listed:
  • Elena-Andreea Florea

    (“Alexandru Ioan Cuza” University)

Abstract

This article aims at studying a special class of constrained vector optimization problems in the setting of a variable ordering structure, having a geometric constraint and finitely many generalized functional constraints. Based on a version of the extended extremal principle, some necessary optimality conditions for a minimal solution of the proposed problem are derived in terms of coderivatives and normal cones.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:1:d:10.1007_s10957-018-1269-6
    DOI: 10.1007/s10957-018-1269-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-1269-6
    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/s10957-018-1269-6?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. Jean-Paul Penot, 1998. "Cooperative behavior of functions, relations and sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 229-246, November.
    2. 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.
    3. 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.
    4. 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.
    5. A. D. Ioffe, 1984. "Necessary Conditions in Nonsmooth Optimization," Mathematics of Operations Research, INFORMS, vol. 9(2), pages 159-189, May.
    6. 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.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Jia-Wei Chen & Zhongping Wan & Yeol Cho, 2013. "Levitin–Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 33-64, February.
    13. 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.
    14. Dmitry Karamzin & Fernando Lobo Pereira, 2019. "On a Few Questions Regarding the Study of State-Constrained Problems in Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 235-255, January.
    15. N. J. Huang & J. Li & J. C. Yao, 2007. "Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 201-212, May.
    16. N. J. Huang & J. Li & S. Y. Wu, 2009. "Optimality Conditions for Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 323-342, August.
    17. 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.
    18. Gang Xiao & Hong Xiao & Sanyang Liu, 2011. "Scalarization and pointwise well-posedness in vector optimization problems," Journal of Global Optimization, Springer, vol. 49(4), pages 561-574, April.
    19. 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.
    20. 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.

    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:178:y:2018:i:1:d:10.1007_s10957-018-1269-6. 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.