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Convergence of Solutions of a Set Optimization Problem in the Image Space

Author

Listed:
  • César Gutiérrez

    (Universidad de Valladolid)

  • Enrico Miglierina

    (Università Cattolica del Sacro Cuore)

  • Elena Molho

    (Università degli Studi di Pavia)

  • Vicente Novo

    (Universidad Nacional de Educación a Distancia (UNED))

Abstract

The present work is devoted to the study of stability in set optimization. In particular, a sequence of perturbed set optimization problems, with a fixed objective map, is studied under suitable continuity assumptions. A formulation of external and internal stability of the solutions is considered in the image space, in such a way that the convergence of a sequence of solutions of perturbed problems to a solution of the original problem is studied under appropriate compactness assumptions. Our results can also be seen as an extension to the set-valued framework of known stability results in vector optimization.

Suggested Citation

  • César Gutiérrez & Enrico Miglierina & Elena Molho & Vicente Novo, 2016. "Convergence of Solutions of a Set Optimization Problem in the Image Space," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 358-371, August.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-016-0942-x
    DOI: 10.1007/s10957-016-0942-x
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    References listed on IDEAS

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    1. S. Li & W. Zhang, 2010. "Hadamard well-posed vector optimization problems," Journal of Global Optimization, Springer, vol. 46(3), pages 383-393, March.
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    4. Jonas Ide & Elisabeth Köbis, 2014. "Concepts of efficiency for uncertain multi-objective optimization problems based on set order relations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 99-127, August.
    5. Loridan, P. & Morgan, J. & Raucci, R., 1997. "Convergence of Minimal and Approximate Minimal Elements of Sets in Partially Ordered Vector Spaces," Papiers d'Economie Mathématique et Applications 97.94, Université Panthéon-Sorbonne (Paris 1).
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    Cited by:

    1. L. Q. Anh & D. V. Hien, 2025. "Convergence of solutions to set optimization problems with variable ordering structures," Journal of Global Optimization, Springer, vol. 91(3), pages 677-699, March.
    2. L. Q. Anh & T. Q. Duy & D. V. Hien, 2020. "Stability of efficient solutions to set optimization problems," Journal of Global Optimization, Springer, vol. 78(3), pages 563-580, November.
    3. Pham Huu Sach & Le Anh Tuan, 2021. "Semicontinuity Property of Approximate Solution Mappings in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 202-228, October.
    4. Lam Quoc Anh & Tran Quoc Duy & Dinh Vinh Hien & Daishi Kuroiwa & Narin Petrot, 2020. "Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 416-432, May.
    5. Yu Han & Kai Zhang & Nan-jing Huang, 2020. "The stability and extended well-posedness of the solution sets for set optimization problems via the Painlevé–Kuratowski convergence," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 175-196, February.

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