Convergence, Scalarization and Continuity of Minimal Solutions in Set Optimization

The paper deals with the study of two different aspects of stability in the given space as well as the image space, where the solution concepts are based on a partial order relation on the family of bounded subsets of a real normed linear space. The first aspect of stability deals with the topologic...

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Bibliographic Details
Published in:Journal of the Operations Research Society of China (Internet) 2024-09, Vol.12 (3), p.773-793
Main Authors: Karuna, Lalitha, C. S.
Format: Article
Language:English
Subjects:
Convergence
Management Science
Mathematics
Mathematics and Statistics
Neighborhoods
Operations Research
Optimization
Set theory
Space
Stability
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Summary:The paper deals with the study of two different aspects of stability in the given space as well as the image space, where the solution concepts are based on a partial order relation on the family of bounded subsets of a real normed linear space. The first aspect of stability deals with the topological set convergence of families of solution sets of perturbed problems in the image space and Painlevé–Kuratowski set convergence of solution sets of the perturbed problems in the given space. The convergence in the given space is also established in terms of solution sets of scalarized perturbed problems. The second aspect of stability deals with semicontinuity of the solution set maps of parametric perturbed problems in both the spaces.
ISSN:2194-668X
2194-6698
DOI:10.1007/s40305-022-00440-6