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New Notions of Proper Efficiency in Set Optimization with the Set Criterion

Author

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  • L. Huerga

    (Universidad Nacional de Educación a Distancia (UNED))

  • B. Jiménez

    (Universidad Nacional de Educación a Distancia (UNED))

  • V. Novo

    (Universidad Nacional de Educación a Distancia (UNED))

Abstract

In this paper, we introduce new notions of proper efficiency in the sense of Henig for a set optimization problem by using the set criterion of solution. The relationships between them are studied. Also, we compare these concepts with the homologous ones given by considering the vector criterion. Finally, a Lagrange multiplier rule for Henig proper solutions of a set optimization problem with a cone constraint is obtained under convexity hypotheses. Illustrative examples are also given.

Suggested Citation

  • L. Huerga & B. Jiménez & V. Novo, 2022. "New Notions of Proper Efficiency in Set Optimization with the Set Criterion," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 878-902, December.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:3:d:10.1007_s10957-022-02088-x
    DOI: 10.1007/s10957-022-02088-x
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    References listed on IDEAS

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    1. J. B. Hiriart-Urruty, 1979. "Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 79-97, February.
    2. B. Jiménez & V. Novo & A. Vílchez, 2020. "Characterization of set relations through extensions of the oriented distance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 89-115, February.
    3. L. Huerga & B. Jiménez & V. Novo & A. Vílchez, 2021. "Six set scalarizations based on the oriented distance: continuity, convexity and application to convex set optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 413-436, April.
    4. X. Y. Zheng, 1997. "Proper Efficiency in Locally Convex Topological Vector Spaces," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 469-486, August.
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