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http://bura.brunel.ac.uk/handle/2438/32365| Title: | Solution Stability and Well-Posedness for Classes of Parametric Set Optimization Problems |
| Authors: | Peng, Z-Y Zeng, Y Chuong, TD Yun, S Yang, X |
| Keywords: | set optimization;improvement set;solution stability;Levitin-Polyak well-posedness;Hadamard well-posedness;49J53;49K40;90C31 |
| Issue Date: | 29-Sep-2025 |
| Publisher: | Springer Nature |
| Citation: | Peng, Z.Y. et al. (2026) 'Solution Stability and Well-Posedness for Classes of Parametric Set Optimization Problems', Journal of Optimization Theory and Applications, 208 (1), 17, pp. 1 - 25. doi: 10.1007/s10957-025-02850-x. |
| 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. |
| Description: | Mathematics Subject Classification: 49J53; 49K40; 90C31. |
| URI: | https://bura.brunel.ac.uk/handle/2438/32365 |
| DOI: | https://doi.org/10.1007/s10957-025-02850-x |
| ISSN: | 0022-3239 |
| Other Identifiers: | ORCiD: Article number: 17 |
| Appears in Collections: | Dept of Mathematics Research Papers |
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