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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)]

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Abstract

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.

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References

  1. Peng, Z.H., Wan, Z.P., Guo, Y.J.: New higher-order weak lower inner epiderivatives and application to Karush–Kuhn–Tucker necessary optimality conditions in set-valued optimization. Japan J. Ind. Appl. Math. 37, 851–866 (2020)

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Acknowledgements

The authors would like to thank anonymous referees for their valuable comments and suggestions, which helped to improve the paper. This research was partially supported by the National Natural Science Foundation of China (No. 11971078) and and the Group Building Project for Scientific Innovation for Universities in Chongqing (CXQT21021).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, 400074, China

    Maoyuan Lv & Qilin Wang

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  1. Maoyuan Lv
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  2. Qilin Wang
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Correspondence to Qilin Wang.

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Lv, M., Wang, Q. 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)]. Japan J. Indust. Appl. Math. 40, 265–273 (2023). https://doi.org/10.1007/s13160-022-00513-2

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  • DOI: https://doi.org/10.1007/s13160-022-00513-2

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