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A Unified Approach Through Image Space Analysis to Robustness in Uncertain Optimization Problems

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Abstract

In this paper, by virtue of the image space analysis, we investigate general scalar robust optimization problems with uncertainties both in the objective and constraints. Under mild assumptions, we characterize various robust solutions for different kinds of robustness concepts, by introducing suitable images of the original uncertain problem, or the images of its counterpart problems appropriately, which provide a unified approach to tackling with robustness for uncertain optimization problems. Several examples are employed to show the effectiveness of the results derived in this paper.

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Acknowledgements

The authors gratefully thank Professor Franco Giannessi, two anonymous referees and the associate editor for their constructive suggestions and detailed comments, which helped to improve the paper and, in particular, thank one referee for pointing out the proof of Theorem 3.2. Also thanks to Manxue You (Chongqing University) for helpful discussions on the image space analysis.

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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 Chun-Rong Chen.

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This research was supported by the National Natural Science Foundation of China (Grant Nos. 11301567, 11571055, 11971078), the Fundamental Research Funds for the Central Universities (Grant No. 106112017CDJZRPY0020) and the Project funded by China Postdoctoral Science Foundation (Grant No. 2019M660247).

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Wei, HZ., Chen, CR. & Li, SJ. A Unified Approach Through Image Space Analysis to Robustness in Uncertain Optimization Problems. J Optim Theory Appl 184, 466–493 (2020). https://doi.org/10.1007/s10957-019-01609-5

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  • DOI: https://doi.org/10.1007/s10957-019-01609-5

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