Generalized Well-Posedness and Stability of Solutions in Set Optimization |
Received:February 24, 2022 Revised:May 08, 2022 |
Key Words:
well-posedness stability set optimization Gerstewitz's function upper semi-continuity lower semi-continuity
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Fund Project:Supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No.KYCX20_1321). |
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Abstract: |
The aim of this paper is to investigate the well-posedness and stability in set optimization. The notion of generalized well-posedness for set optimization problems is introduced using the embedding technique for the first time. Some criteria and characterizations of this type of well-posedness are derived. Sufficient conditions are also given for this type of well-posedness. Moreover, by virtue of a generalized Gerstewitz's function, the equivalent relation between this type of well-posedness and the generalized well-posedness of a scalar optimization problem is established. Finally, the upper semi-continuity and lower semi-continuity of weak efficient solution mappings for parametric set optimization problems are investigated under some suitable conditions. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2022.06.008 |
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