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S-Derivative of the Extremum Multifunction to a Multi-objective Parametric Discrete Optimal Control Problem

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Abstract

In this paper, we derive formulae for computing the S-derivative of the extremum multifunction in a multi-objective parametric discrete optimal control problem with nonconvex objective functions and control constraints. Particularly, we obtain formulae for upper and lower evaluation on the S-derivative of the extremum multifunction via the solution of state equations, the tangent cone to the constraint sets, and the Fréchet derivative of the objective functions. By establishing an abstract result on the S-derivative of the extremum multifunction in a multi-objective parametric mathematical programming problem, we derive formulae for upper and lower evaluation on the S-derivative of the extremum multifunction in a multi-objective parametric discrete optimal control problem.

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Acknowledgements

The authors would like to thank the editor and referee for careful reading and constructive comments. In this research, the first author was partially supported by the Vietnam Ministry of Education and Training and Vietnam Institute for advanced study in Mathematics under the grant B2022-CTT-05.

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  1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam

    Nguyen Thi Toan & Le Quang Thuy

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  1. Nguyen Thi Toan
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  2. Le Quang Thuy
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Correspondence to Nguyen Thi Toan.

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Communicated by Jen-Chih Yao.

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Toan, N.T., Thuy, L.Q. S-Derivative of the Extremum Multifunction to a Multi-objective Parametric Discrete Optimal Control Problem. J Optim Theory Appl 196, 240–265 (2023). https://doi.org/10.1007/s10957-022-02130-y

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