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Stability of efficient solutions to set optimization problems

Author

Listed:
  • L. Q. Anh

    (Cantho University)

  • T. Q. Duy

    (Ton Duc Thang University
    Ton Duc Thang University)

  • D. V. Hien

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

Abstract

This article deals with considering stability properties of Pareto minimal solutions to set optimization problems with the set less order relation in real topological Hausdorff vector spaces. We focus on studying the Painlevé–Kuratowski convergence of Pareto minimal elements in the image space. Employing convexity properties, we study the external stability of Pareto minimal solutions via weak ones. Then, we use converse properties to investigate external stability conditions to such problems where Pareto minimal solution sets and weak/ideal ones are distinct. For the internal stability, we propose a concept of compact convergence in the sense of Painlevé–Kuratowski and use it together with a domination property to analyze stability conditions for the reference problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:78:y:2020:i:3:d:10.1007_s10898-020-00932-w
    DOI: 10.1007/s10898-020-00932-w
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    References listed on IDEAS

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    5. 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.
    6. Nithirat Sisarat & Rabian Wangkeeree & Gue Myung Lee, 2020. "On Set Containment Characterizations for Sets Described by Set-Valued Maps with Applications," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 824-841, March.
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    8. Duong Thi Kim Huyen & Jen-Chih Yao & Nguyen Dong Yen, 2019. "Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 1: Lipschitzian Stability," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 91-116, January.
    9. Duong Thi Kim Huyen & Jen-Chih Yao & Nguyen Dong Yen, 2019. "Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 2: Robinson Stability," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 117-139, January.
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