Abstract
In this paper, we deal with robust optimal solution sets for a class of optimization problems with data uncertainty in both the objective and constraints. We first introduce a mixed-type robust dual problem of this class of uncertain optimization problems and explore robust strong duality relations between them. Then, we propose a new approach to characterize robust optimal solution sets of this class of uncertain optimization problems via its dual problem. Moreover, we show that several results on characterizations of robust optimal solution sets of uncertain optimization problems obtained in recent literature can be obtained using our approach.
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Acknowledgements
We would like to express our sincere thanks to the anonymous referees for many helpful comments and constructive suggestions which have contributed to the final preparation of this paper. This research was supported by the Basic and Advanced Research Project of Chongqing (cstc2017jcyjBX0032, cstc2016jcyjAX0178), the ARC Discovery Grant (DP190103361), the National Natural Science Foundation of China (11701057 and 11471059), and the Program for University Innovation Team of Chongqing (CXTDX201601026).
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Communicated by Xinmin Yang.
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Sun, X., Teo, K.L. & Tang, L. Dual Approaches to Characterize Robust Optimal Solution Sets for a Class of Uncertain Optimization Problems. J Optim Theory Appl 182, 984–1000 (2019). https://doi.org/10.1007/s10957-019-01496-w
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DOI: https://doi.org/10.1007/s10957-019-01496-w