A note on “New higher-order weak lower inner epiderivatives and application to Karush–Kuhn–Tucker necessary optimality conditions in set-valued optimization” [Japan Journal of Industrial and Applied Mathematics. 37, 851–866 (2020)]

In this note, we establish a property of higher-order weak lower inner Studniarski epiderivative. By virtue of the property, we demonstrate that Proposition 2 in Peng et al. (Japan J Ind Appl Math 37:851–866, 2020) is incorrect, and provide a modification of the proposition. An example is given to i...

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Bibliographic Details
Published in:Japan journal of industrial and applied mathematics 2023-01, Vol.40 (1), p.265-273
Main Authors: Lv, Maoyuan, Wang, Qilin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Optimization
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Summary:In this note, we establish a property of higher-order weak lower inner Studniarski epiderivative. By virtue of the property, we demonstrate that Proposition 2 in Peng et al. (Japan J Ind Appl Math 37:851–866, 2020) is incorrect, and provide a modification of the proposition. An example is given to illustrate the modified result. Some remarks are given on the results in this note.
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-022-00513-2