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On higher-order proto-differentiability of perturbation maps

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Abstract

This paper is concerned with higher-order sensitivity analysis in parametric vector optimization problems. Firstly, higher-order proto-differentiability of a set-valued mapping from one Euclidean space to another is defined. Then, we prove that the perturbation map/the proper perturbation map/the weak perturbation map of a parameterized vector optimization problem are higher-order proto-differentiable under some suitable qualification conditions.

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Acknowledgements

The author would like to thank the Editors for the help in the processing of the article. The author is very grateful to the Associate Editor and the Anonymous Referee for the valuable remarks, which helped to improve the paper. This work is partially supported by Can Tho University.

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  1. Department of Mathematics, College of Natural Sciences, Can Tho University, Can Tho, 900000, Vietnam

    L. T. Tung

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Tung, L.T. On higher-order proto-differentiability of perturbation maps. Positivity 24, 441–462 (2020). https://doi.org/10.1007/s11117-019-00689-x

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