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Optimality Conditions for Nondifferentiable Minimax Programs and Vector Optimization Problems

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Abstract

First-order sufficient optimality conditions in terms of Lagrangian functions and Lagrange multipliers for nondifferentiable minimax programs and vector optimization problems in an Asplund space setting are obtained in this paper. Two illustrative examples are given. Our results implement the first-order necessary optimality conditions of Chuong and Kim (Ann Oper Res 251:73–87, 2017).

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Acknowledgements

This research was supported by PHENIKAA University, the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (NRF-2019R1A2C1008672), and Vietnam Academy of Science and Technology. D.T.K. Huyen is grateful to Hanoi Pedagogical University 2 for creating favorable working conditions for her. The authors would like to thank the Area Editor and the anonymous referee for their useful suggestions, which have helped to improve the presentation of the paper.

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Authors and Affiliations

  1. ORLab, Faculty of Computer Science, Phenikaa University, Hanoi, 12116, Vietnam

    Duong Thi Kim Huyen

  2. Department of Applied Mathematics, Pukyong National University, Busan, Republic of Korea

    Do Sang Kim

  3. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, 10307, Vietnam

    Nguyen Dong Yen

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  1. Duong Thi Kim Huyen
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  2. Do Sang Kim
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  3. Nguyen Dong Yen
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Correspondence to Do Sang Kim.

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Communicated by René Henrion.

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Huyen, D.T.K., Kim, D.S. & Yen, N.D. Optimality Conditions for Nondifferentiable Minimax Programs and Vector Optimization Problems. J Optim Theory Appl 200, 703–723 (2024). https://doi.org/10.1007/s10957-023-02366-2

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