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Minimax programming as a tool for studying robust multi-objective optimization problems

Author

Listed:
  • Zhe Hong

    (Yanbian University
    Pukyong National University)

  • Kwan Deok Bae

    (Pukyong National University)

  • Do Sang Kim

    (Pukyong National University)

Abstract

This paper aims to investigate optimality conditions for a weakly Pareto solution to a robust multi-objective optimization problem with locally Lipschitzian data. We do this by using a minimax programming approach, namely, by establishing the necessary optimality condition for a (local) optimal solution to a robust minimax optimization problem under a suitable constraint qualification, we then employ it to arrive in the desired target. In addition, some duality results for both robust minimax optimization problems and robust multi-objective optimization problems are also provided.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:319:y:2022:i:2:d:10.1007_s10479-021-04179-w
    DOI: 10.1007/s10479-021-04179-w
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    References listed on IDEAS

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    1. Thai Doan Chuong & Do Sang Kim, 2016. "A class of nonsmooth fractional multiobjective optimization problems," Annals of Operations Research, Springer, vol. 244(2), pages 367-383, September.
    2. Jiawei Chen & Elisabeth Köbis & Jen-Chih Yao, 2019. "Optimality Conditions and Duality for Robust Nonsmooth Multiobjective Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 411-436, May.
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    6. Thai Chuong & Do Kim, 2014. "Optimality conditions and duality in nonsmooth multiobjective optimization problems," Annals of Operations Research, Springer, vol. 217(1), pages 117-136, June.
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    Cited by:

    1. 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.

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