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Constraint qualifications and optimality conditions for robust nonsmooth semi-infinite multiobjective optimization problems

Author

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  • Nguyen Minh Tung

    (Banking University of Ho Chi Minh City)

  • Mai Duy

    (FPT University)

Abstract

In this paper, for a robust nonsmooth semi-infinite objective optimization problem associated with data uncertainty, some constraint qualifications (CQs): Abadie CQ, Mangasarian-Fromovitz CQ, and Pshenichnyi-Levin-Valadire CQ are proposed. Sufficient conditions for them are also derived. Under these CQs, we establish both necessary and sufficient conditions for robust weak Pareto, Pareto, and Benson proper solutions. These conditions are the forms of Karush-Kuhn-Tucker rule. Moreover, the Wolfe and Mond-Weir duality schemes are also addressed. Finally, we employ the obtained results to present some conditions for linear programming. Examples are provided for analyzing and illustrating our results.

Suggested Citation

  • Nguyen Minh Tung & Mai Duy, 2023. "Constraint qualifications and optimality conditions for robust nonsmooth semi-infinite multiobjective optimization problems," 4OR, Springer, vol. 21(1), pages 151-176, March.
    • Handle: RePEc:spr:aqjoor:v:21:y:2023:i:1:d:10.1007_s10288-022-00506-4
    DOI: 10.1007/s10288-022-00506-4
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    References listed on IDEAS

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    1. 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.
    2. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, October.
    3. Jae Hyoung Lee & Gue Myung Lee, 2018. "On optimality conditions and duality theorems for robust semi-infinite multiobjective optimization problems," Annals of Operations Research, Springer, vol. 269(1), pages 419-438, October.
    4. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2015. "Robust solutions to multi-objective linear programs with uncertain data," European Journal of Operational Research, Elsevier, vol. 242(3), pages 730-743.
    5. Jeyakumar, V. & Li, G., 2010. "New strong duality results for convex programs with separable constraints," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1203-1209, December.
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