The stability of the solution sets for set optimization problems via improvement sets

The aim of this paper is to investigate the stability of the solution sets for set optimization problems via improvement sets. Firstly, we consider the relations among the solution sets for optimization problem with set optimization criterion. Then, the closeness and the convexity of solution sets a...

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Bibliographic Details
Published in:Optimization 2019-11, Vol.68 (11), p.2171-2193
Main Authors: Mao, Jia-yu, Wang, San-hua, Han, Yu
Format: Article
Language:English
Subjects:
Continuity
Convexity
improvement set
lower semi-continuity
Optimization
Parametric set optimization problem
solution mapping
Stability
upper semi-continuity
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Summary:The aim of this paper is to investigate the stability of the solution sets for set optimization problems via improvement sets. Firstly, we consider the relations among the solution sets for optimization problem with set optimization criterion. Then, the closeness and the convexity of solution sets are discussed. Furthermore, the upper semi-continuity, Hausdorff upper semi-continuity and lower semi-continuity of solution mappings to parametric set optimization problems via improvement sets are established under some suitable conditions. These results extend and develop some recent works in this field.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2019.1579813