Abstract
In this paper, we obtain the Painlevé–Kuratowski upper convergence and the Painlevé–Kuratowski lower convergence of the approximate solution sets for set optimization problems with the continuity and convexity of objective mappings. Moreover, we discuss the extended well-posedness and the weak extended well-posedness for set optimization problems under some mild conditions. We also give some examples to illustrate our main results.
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The authors are grateful to the editors and reviewers whose helpful comments and suggestions have led to much improvement of the paper.
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This work was supported by the National Natural Science Foundation of China (11471230, 11671282, 11801257).
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Han, Y., Zhang, K. & Huang, Nj. The stability and extended well-posedness of the solution sets for set optimization problems via the Painlevé–Kuratowski convergence. Math Meth Oper Res 91, 175–196 (2020). https://doi.org/10.1007/s00186-019-00695-5
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DOI: https://doi.org/10.1007/s00186-019-00695-5