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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. Ehrgott, Matthias & Ide, Jonas & Schöbel, Anita, 2014. "Minmax robustness for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 239(1), pages 17-31.
    3. 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.
    4. Hang-Chin Lai & Tone-Yau Huang, 2012. "Nondifferentiable minimax fractional programming in complex spaces with parametric duality," Journal of Global Optimization, Springer, vol. 53(2), pages 243-254, June.
    5. 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.
    6. 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.
    7. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    8. T. Son & D. Kim, 2013. "ε-Mixed type duality for nonconvex multiobjective programs with an infinite number of constraints," Journal of Global Optimization, Springer, vol. 57(2), pages 447-465, October.
    9. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    10. Thai Doan Chuong & Do Sang Kim, 2018. "Normal regularity for the feasible set of semi-infinite multiobjective optimization problems with applications," Annals of Operations Research, Springer, vol. 267(1), pages 81-99, August.
    11. Liguo Jiao & Jae Hyoung Lee, 2021. "Finding efficient solutions in robust multiple objective optimization with SOS-convex polynomial data," Annals of Operations Research, Springer, vol. 296(1), pages 803-820, January.
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