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Optimality conditions and sensitivity analysis in parametric nonconvex minimax programming

Author

Listed:
  • D. T. V. An

    (Thai Nguyen University of Sciences)

  • N. H. Hung

    (Hanoi Pedagogical University 2, Xuan Hoa)

  • D. T. Ngoan

    (Hanoi University of Natural Resources and Environment)

  • N. V. Tuyen

    (Hanoi Pedagogical University 2, Xuan Hoa)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:90:y:2024:i:1:d:10.1007_s10898-024-01388-y
    DOI: 10.1007/s10898-024-01388-y
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    References listed on IDEAS

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    1. Duong Thi Viet An & Abderrahim Jourani, 2022. "Subdifferentials of the Marginal Functions in Parametric Convex Optimization via Intersection Formulas," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 82-96, January.
    2. 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.
    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.
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