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Optimality conditions and sensitivity analysis in parametric nonconvex minimax programming

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Abstract

In this paper, we perform optimality conditions and sensitivity analysis for parametric nonconvex minimax programming problems. Our aim is to study the necessary optimality conditions by using the Mordukhovich (limiting) subdifferential and to give upper estimations for the Mordukhovich subdifferential of the optimal value function in the problem under consideration. The optimality conditions and sensitivity analysis are obtained by using upper estimates for Mordukhovich subdifferentials of the maximum function. The results on optimality conditions are then applied to parametric multiobjective optimization problems. An example is given to illustrate our results.

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Acknowledgements

The authors would like to thank the anonymous referee for careful readings and valuable suggestions which improved the presentation of this manuscript.

Funding

The first author was supported by the Science and Technology Fund of the Vietnam Ministry of Education and Training (B2024-TNA-20).

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Thai Nguyen University of Sciences, Thai Nguyen, 250000, Vietnam

    D. T. V. An

  2. Department of Mathematics, Hanoi Pedagogical University 2, Xuan Hoa, Phuc Yen, Vinh Phuc, Vietnam

    N. H. Hung & N. V. Tuyen

  3. Department of Basic Sciences, Hanoi University of Natural Resources and Environment, 11916, Hanoi, Vietnam

    D. T. Ngoan

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  1. D. T. V. An
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  2. N. H. Hung
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  3. D. T. Ngoan
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  4. N. V. Tuyen
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Correspondence to N. V. Tuyen.

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An, D.T.V., Hung, N.H., Ngoan, D.T. et al. Optimality conditions and sensitivity analysis in parametric nonconvex minimax programming. J Glob Optim (2024). https://doi.org/10.1007/s10898-024-01388-y

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