Solution Stability and Well-Posedness for Classes of Parametric Set Optimization Problems
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.
Authors
- Sangwoon Yun (ORCID: https://orcid.org/0000-0002-5782-7266)
- Thái Doãn Chương (ORCID: https://orcid.org/0000-0003-0893-5604)
- Xin Yang (ORCID: https://orcid.org/0000-0001-8691-8995)
- Yué Zeng (ORCID: https://orcid.org/0000-0003-0124-646X)
- Zai-Yun Peng
Institutions
- Yunnan Normal University (CN)
- Sichuan University (CN)
- Brunel University of London (GB)
- Chongqing Jiaotong University (CN)
- Sungkyunkwan University (KR)
Publication Details
- Journal
- Journal of Optimization Theory and Applications
- Published
- 2025-09-29
- DOI
- https://doi.org/10.1007/s10957-025-02850-x
- Citations
- 2
- Primary Topic
- Optimization and Variational Analysis
- Type
- article
- Field-Weighted Citation Impact
- 3.01
Funders
- National Natural Science Foundation of China
- Chongqing Municipal Education Commission
- Chongqing Jiaotong University
- Centre Scientifique et Technique du Bâtiment