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Set Approach for Set Optimization with Variable Ordering Structures Part II: Scalarization Approaches

Author

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  • Gabriele Eichfelder

    (Technische Universität Ilmenau)

  • Maria Pilecka

    (Technische Universität Bergakademie Freiberg)

Abstract

This paper combines variable ordering structures with set relations in set optimization. We continue our examinations of set optimization problems and use the optimality notions as well as the set relations introduced in the paper (Eichfelder and Pilecka in Set Approach for Set Optimization with Variable Ordering Structures Part I: Set Relations and Relationship to Vector Approach, 2016). We present linear scalarization results and a new nonlinear scalarization approach for set relations. Moreover, we introduce some additional set relations which allow us to investigate connections between our results, based on the set approach, and others presented in the literature which are based on the vector approach. This gives us the possibility to apply the optimality conditions derived there to our concepts.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:3:d:10.1007_s10957-016-0993-z
    DOI: 10.1007/s10957-016-0993-z
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    References listed on IDEAS

    as
    1. Johannes Jahn, 2015. "Vectorization in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 783-795, December.
    2. Gabriele Eichfelder, 2014. "Numerical Procedures in Multiobjective Optimization with Variable Ordering Structures," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 489-514, August.
    3. 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.
    4. 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.
    5. 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.
    6. Johannes Jahn, 2015. "A derivative-free descent method in set optimization," Computational Optimization and Applications, Springer, vol. 60(2), pages 393-411, March.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. 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.
    2. Khushboo & C. S. Lalitha, 2023. "Characterizations of set order relations and nonlinear scalarizations via generalized oriented distance function in set optimization," Journal of Global Optimization, Springer, vol. 85(1), pages 235-249, January.
    3. 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.

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