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Robustness Characterizations for Uncertain Optimization Problems via Image Space Analysis

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Abstract

In this paper, by means of linear and nonlinear (regular) weak separation functions, we obtain some characterizations of robust optimality conditions for uncertain optimization problems, especially saddle point sufficient optimality conditions. Additionally, the relationships between three approaches used for robustness analysis: image space analysis, vector optimization and set-valued optimization, are discussed. Finally, an application for finding a shortest path is given to verify the validity of the results derived in this paper.

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Acknowledgements

The authors gratefully thank the Editor-in-Chief and two anonymous referees for their constructive suggestions and detailed comments, which helped to improve the paper. Particularly, they thank one referee for pointing out that the relations between the ISA approach and tools from vector optimization and set-valued optimization could be explored (see Sects. 4.1 and 4.2, where Theorem 4.1 has been presented by one referee). Also they thank to Manxue You (Chongqing University) for helpful discussions on the image space analysis. This research was supported by the Project funded by China Postdoctoral Science Foundation (Grant No. 2019M660247), the Fundamental Research Funds for the Central Universities (Grant Nos. GK202003010, 106112017CDJZRPY0020) and the National Natural Science Foundation of China (Grant No. 11971078).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Hong-Zhi Wei

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Chun-Rong Chen & Sheng-Jie Li

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  1. Hong-Zhi Wei
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  2. Chun-Rong Chen
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  3. Sheng-Jie Li
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Correspondence to Hong-Zhi Wei.

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Wei, HZ., Chen, CR. & Li, SJ. Robustness Characterizations for Uncertain Optimization Problems via Image Space Analysis. J Optim Theory Appl 186, 459–479 (2020). https://doi.org/10.1007/s10957-020-01709-7

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