Abstract
This paper investigates optimality conditions and duality for a class of convex adjustable robust optimization problem (ARP). We first propose some constraint qualifications (CQs): the Abadie CQ, the local Farkas–Minkowski CQ, Mangasarian-Fromovitz CQ, and Slater CQ; and give some relationships between these CQs. Then we employ them to derive necessary and sufficient optimality conditions for the optimal solution of (ARP). These conditions are form of Karush–Kuhn–Tucker multiplier rules. We also introduce the Wolfe and Mond-Weir duality schemes and discuss weak, strong, and converse duality results. As an application, some optimality conditions for robust optimization problem are obtained. We include many examples for analyzing and illustrating our results.
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Acknowledgements
The authors are very grateful to the Editors and the Anonymous Referees for their valuable suggestions and remarks leading to the significant improvement of the paper. This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under Grant number B2024-20-36. A part of this work was completed during a research stay of the first author at Vietnam Institute for Advanced Study in Mathematics (VIASM). They are warmly grateful to this institute for its hospitality and support.
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Tung, N.M., Van Duy, M. & Dai, L.X. Karush–Kuhn–Tucker conditions and duality for a class of convex adjustable robust optimization problem. Comp. Appl. Math. 43, 245 (2024). https://doi.org/10.1007/s40314-024-02762-y
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DOI: https://doi.org/10.1007/s40314-024-02762-y