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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月29日

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  • Zai-Yun Peng,
  • Yue Zeng,
  • Thai Doan Chuong,
  • Sangwoon Yun,
  • Xin Yang

摘要

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.