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Solution Stability and Well-Posedness for Classes of Parametric Set Optimization Problems

Author

Listed:
  • Zai-Yun Peng

    (Yunnan Normal University
    Yunnan Normal University
    Chongqing JiaoTong University)

  • Yue Zeng

    (Sichuan University)

  • Thai Doan Chuong

    (Department of Mathematics, Brunel University of London)

  • Sangwoon Yun

    (Sungkyunkwan University)

  • Xin Yang

    (Chongqing JiaoTong University)

Abstract

This paper investigates the solution stability and well-posedness for a parametric set optimization problem (PSOP), where lower and upper set order relations are induced by an improvement set. We provide new sufficient conditions for the outer-continuity, outer-openness and inner-openness of the solution mapping of (PSOP). By utilizing the property of cone-continuity, we derive sufficient conditions ensuring the Levitin-Polyak well-posedness for (PSOP) and the Hadamard well-posedness for a related parametric implicit set optimization problem (ISOP). Numerical examples are also given to illustrate the main results.

Suggested Citation

  • Zai-Yun Peng & Yue Zeng & Thai Doan Chuong & Sangwoon Yun & Xin Yang, 2026. "Solution Stability and Well-Posedness for Classes of Parametric Set Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-25, January.
    • Handle: RePEc:spr:joptap:v:208:y:2026:i:1:d:10.1007_s10957-025-02850-x
    DOI: 10.1007/s10957-025-02850-x
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