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Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation

Author

Listed:
  • Lam Quoc Anh

    (Cantho University)

  • Tran Quoc Duy

    (Ton Duc Thang University
    Ton Duc Thang University)

  • Dinh Vinh Hien

    (University of Science, Vietnam National University Ho Chi Minh City
    Ho Chi Minh City University of Food Industry)

  • Daishi Kuroiwa

    (Shimane University)

  • Narin Petrot

    (Naresuan University)

Abstract

This article investigates stability conditions for set optimization problems with the set less order relation in the senses of Panilevé–Kuratowski and Hausdorff convergence. Properties of various kinds of convergences for elements in the image space are discussed. Taking such properties into account, formulations of internal and external stability of the solutions are studied in the image space in terms of the convergence of a solution sets sequence of perturbed set optimization problems to a solution set of the given problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:2:d:10.1007_s10957-020-01657-2
    DOI: 10.1007/s10957-020-01657-2
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    References listed on IDEAS

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    1. 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.
    2. Yu Han & Nan-jing Huang, 2018. "Continuity and Convexity of a Nonlinear Scalarizing Function in Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 679-695, June.
    3. Johannes Jahn, 2017. "Karush–Kuhn–Tucker Conditions in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 707-725, March.
    4. Giovanni P. Crespi & Mansi Dhingra & C. S. Lalitha, 2018. "Pointwise and global well-posedness in set optimization: a direct approach," Annals of Operations Research, Springer, vol. 269(1), pages 149-166, October.
    5. Y. D. Xu & S. J. Li, 2016. "On the solution continuity of parametric set optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 223-237, August.
    6. Michel H. Geoffroy, 2019. "A topological convergence on power sets well-suited for set optimization," Journal of Global Optimization, Springer, vol. 73(3), pages 567-581, March.
    7. S. Khoshkhabar-amiranloo & E. Khorram, 2015. "Pointwise well-posedness and scalarization in set optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(2), pages 195-210, October.
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    Cited by:

    1. 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.
    2. Chuang-Liang Zhang & Nan-jing Huang, 2021. "Set Relations and Weak Minimal Solutions for Nonconvex Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 894-914, September.

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