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Vectorization in Set Optimization

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  • Johannes Jahn

    (Universität Erlangen-Nürnberg)

Abstract

In analogy to the scalarization principle in vector optimization, this paper presents a new vectorization approach for set optimization problems. Vectorization means the replacement of a set optimization problem by a suitable vector optimization problem. This approach is developed for the set less order relation used by Kuroiwa and the minmax less order relation introduced by Ha and Jahn.

Suggested Citation

  • Johannes Jahn, 2015. "Vectorization in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 783-795, December.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:3:d:10.1007_s10957-013-0363-z
    DOI: 10.1007/s10957-013-0363-z
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    Citations

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    Cited by:

    1. 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.
    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. Johannes Jahn, 2022. "Characterizations of the Set Less Order Relation in Nonconvex Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 523-544, June.
    4. Johannes Jahn, 2017. "Karush–Kuhn–Tucker Conditions in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 707-725, March.
    5. Elisabeth Köbis & Markus A. Köbis & Xiaolong Qin, 2020. "An Inequality Approach to Approximate Solutions of Set Optimization Problems in Real Linear Spaces," Mathematics, MDPI, vol. 8(1), pages 1-17, January.
    6. 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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