Continuity of the solutions sets for parametric set optimization problems

The current study focuses on exploring the stability of solution sets pertaining to set optimization problems, particularly with regard to the set order relation outlined by Karaman et al. 2018 . Sufficient conditions are provided for the lower semicontinuity, upper semicontinuity, and compactness o...

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Bibliographic Details
Published in:Journal of inequalities and applications 2024-04, Vol.2024 (1), p.62-12, Article 62
Main Authors: Yang, Manli, Li, Taiyong, Xu, Guanghui
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Applied mathematics
Locally Lipschitz continuity
Mathematics
Mathematics and Statistics
Optimization
Semicontinuity
Set optimization
Stability
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Summary:The current study focuses on exploring the stability of solution sets pertaining to set optimization problems, particularly with regard to the set order relation outlined by Karaman et al. 2018 . Sufficient conditions are provided for the lower semicontinuity, upper semicontinuity, and compactness of m -minimal solution mappings in parametric set optimization, where the involved set-valued mapping is Lipschitz continuous.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-024-03138-w