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Optimality Conditions at Infinity for Nonsmooth Minimax Programming Problems with Some Applications

Author

Listed:
  • Nguyen Tuyen

    (Hanoi Pedagogical University 2)

  • Kwan Deok Bae

    (Pukyong National University)

  • Do Sang Kim

    (Pukyong National University)

Abstract

This paper is devoted to the study of optimality conditions at infinity in nonsmooth minimax programming problems and their applications. By means of the limiting subdifferential and the normal cone at infinity, we derive necessary and sufficient optimality conditions of the Karush–Kuhn–Tucker type for nonsmooth minimax programming problems with constraints. The obtained results are applied to nonsmooth vector optimization problems and robust minimax optimization ones.

Suggested Citation

  • Nguyen Tuyen & Kwan Deok Bae & Do Sang Kim, 2025. "Optimality Conditions at Infinity for Nonsmooth Minimax Programming Problems with Some Applications," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-22, May.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02652-1
    DOI: 10.1007/s10957-025-02652-1
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    References listed on IDEAS

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    1. Zhe Hong & Kwan Deok Bae & Do Sang Kim, 2022. "Minimax programming as a tool for studying robust multi-objective optimization problems," Annals of Operations Research, Springer, vol. 319(2), pages 1589-1606, December.
    2. Duong Thi Kim Huyen & Do Sang Kim & Nguyen Dong Yen, 2024. "Optimality Conditions for Nondifferentiable Minimax Programs and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 200(2), pages 703-723, February.
    3. Thai Doan Chuong & Do Sang Kim, 2017. "Nondifferentiable minimax programming problems with applications," Annals of Operations Research, Springer, vol. 251(1), pages 73-87, April.
    4. D. T. V. An & N. H. Hung & D. T. Ngoan & N. V. Tuyen, 2024. "Optimality conditions and sensitivity analysis in parametric nonconvex minimax programming," Journal of Global Optimization, Springer, vol. 90(1), pages 53-72, September.
    Full references (including those not matched with items on IDEAS)

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