Abstract
In this paper, under some suitable assumptions without any involving information on the solution set, we give some sufficient conditions for the upper semicontinuity, lower semicontinuity, and closedness of the solution set mapping to a parametric set optimization problem with possible less order relation.
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The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which helped improve the paper.
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This research was supported by the National Natural Science Foundation of China (No. 11426055), the Science and Technology Research Project of Chongqing Municipal Education Commission (No. KJ1500419), the Basic and Advanced Research Project of Chongqing Science and Technology Commission (No. cstc2014jcyjA00044), and the Doctor Start-up Foundation of Chongqing University of Posts and Telecommunications (No. A2014-15).
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Xu, YD., Zhang, PP. On the Stability of the Solution Set Mappings to Parametric Set Optimization Problems. J. Oper. Res. Soc. China 4, 255–263 (2016). https://doi.org/10.1007/s40305-015-0110-2
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DOI: https://doi.org/10.1007/s40305-015-0110-2
Keywords
- Upper semicontinuity
- Lower semicontinuity
- Closedness
- Parametric set optimization problem
- Less order relation