Abstract
The aim of this paper is to study the stability of perturbed set optimization problems via general ordering sets. Firstly, for a set optimization problem (SOP) via general ordering sets, four kinds of concepts about the minimal solutions of (SOP) are given. Then, some properties of the four kinds of solution sets and the level set of objective mappings are investigated. Finally, by employing the recession cone technique, sufficient conditions of upper Painlevé–Kuratowski convergence of minimal approximate solution sets, Painlevé–Kuratowski convergence of weak minimal approximate solution sets of (SOP) are obtained, where the feasible set is perturbed. Some examples are given to illustrate the mainly results in the paper.
Funding Statement
The first author was partially supported by the National Natural Science Foundation of China (12271067), the Chongqing Natural Science Foundation (cstc2021jcyj-msxmX0080), the Group Building Scientific Innovation Project for Universities in Chongqing (CXQT21021) and the Science and Technology Research Program of Chongqing Municipal Education Commission (KJZD-K202200704). The second author was partially supported by the Postgraduate Research and Innovation Project of Chongqing Jiaotong University (2021S0062). The third author was partially supported by the Joint Training Base Construction Project for Graduate Students in Chongqing (JDLHPYJD2021016).
Acknowledgments
The work of the first author was completed during his visit to the Shenzhen Research Institute of Big Data, Chinese University of Hong Kong, Shenzhen, China, to which he is grateful to the hospitality received.
Citation
Zai-Yun Peng. Chong-Yang Shao. Yue Zeng. Yi-Bin Xiao. "Painlevé–Kuratowski Stability of Approximate Solution Sets for Perturbed Set Optimization Problems Under General Ordering Sets by Recession Cone." Taiwanese J. Math. 28 (3) 611 - 636, June, 2024. https://doi.org/10.11650/tjm/240104
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