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.
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Acknowledgements
The authors are very grateful to the Editor and the anonymous referees for their valuable remarks and suggestions. This work was supported by the National Foundation for Science and Technology Development (NAFOSTED) of Vietnam under Grant 101.01-2021.13.
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Tung, N.M., Van Duy, M. Constraint qualifications and optimality conditions for robust nonsmooth semi-infinite multiobjective optimization problems. 4OR-Q J Oper Res 21, 151–176 (2023). https://doi.org/10.1007/s10288-022-00506-4
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DOI: https://doi.org/10.1007/s10288-022-00506-4
Keywords
- Robust multiobjective optimization
- Semi-infinite optimization
- Optimality condition
- Duality
- Constraint qualification