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Generalized higher-order semi-derivative of the perturbation maps in vector optimization

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Abstract

In the present paper, we focus on the higher-order sensitivity analysis in parametric vector optimization problems. We prove that the Borwein proper efficient solution maps/the Borwein proper efficient perturbation maps of a parametric vector optimization problem are generalized higher-order semi-differentiable under some suitable qualification conditions. Several examples are given to illustrate the obtained results.

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Acknowledgements

The author would like to thank Professor Akihisa Tamura for the help in the processing of the article. The author is very grateful to two Anonymous Referees for many valuable comments and suggestions to improve the original version of the article.

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  1. Faculty of Pedagogy and Faculty of Social Sciences and Humanities, Kien Giang University, Chau Thanh, Kien Giang, Vietnam

    Thanh-Hung Pham

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Pham, TH. Generalized higher-order semi-derivative of the perturbation maps in vector optimization. Japan J. Indust. Appl. Math. 40, 929–963 (2023). https://doi.org/10.1007/s13160-022-00560-9

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  • DOI: https://doi.org/10.1007/s13160-022-00560-9

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