In this paper, we investigate set optimization problems with three types of set order relations. Various kinds of well-posedness for these problems and their relationship are concerned. Then, sufficient conditions for set optimization problems to be well-posed are established. Moreover, Kuratowski measure of noncompactness is applied to survey characterizations of well-posedness for set optimization problems. Furthermore, approximating solution maps and their stability are researched to propose the link between stability of the approximating problem and well-posedness of the set optimization problem.
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We are very grateful to the referees for the valuable and detailed remarks and suggestions that helped us significantly improve the paper.
Rabian Wangkeeree was partially supported by the Thailand Research Fund, Grant No. RSA6080077 and Naresuan University. The second author was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED), Grant No. 101.01-2017.18.
Dedicated to Professor Hoang Tuy
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Vui, P.T., Anh, L.Q. & Wangkeeree, R. Well-Posedness for Set Optimization Problems Involving Set Order Relations. Acta Math Vietnam 45, 329–344 (2020). https://doi.org/10.1007/s40306-020-00362-6
- Set order relation
- Set optimization problem
- Measure of noncompactness
Mathematics Subject Classification (2010)