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Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure

Author

Listed:
  • Shokouh Shahbeyk

    (University of Tehran)

  • Majid Soleimani-damaneh

    (University of Tehran)

  • Refail Kasimbeyli

    (Anadolu University)

Abstract

In this paper, we introduce Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure. We prove the connections between Benson properly nondominated, Hartley properly nondominated, and super nondominated solutions under appropriate assumptions. Moreover, we establish some necessary and sufficient conditions for newly-defined solutions invoking an augmented dual cone approach, the linear scalarization, and variational analysis tools. In addition to the theoretical results, various clarifying examples are given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:2:d:10.1007_s10898-018-0614-5
    DOI: 10.1007/s10898-018-0614-5
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    References listed on IDEAS

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    1. Luc, Dinh The & Soubeyran, Antoine, 2013. "Variable preference relations: Existence of maximal elements," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 251-262.
    2. Kazhal Khaledian & Esmaile Khorram & Majid Soleimani-damaneh, 2016. "Strongly Proper Efficient Solutions: Efficient Solutions with Bounded Trade-Offs," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 864-883, March.
    3. Refail Kasimbeyli, 2013. "A conic scalarization method in multi-objective optimization," Journal of Global Optimization, Springer, vol. 56(2), pages 279-297, June.
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    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
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    Cited by:

    1. 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.
    2. Refail Kasimbeyli & Masoud Karimi, 2021. "Duality in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 139-160, May.

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