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Characterizations for Optimality Conditions of General Robust Optimization Problems

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Abstract

In this paper, by virtue of the image space analysis, the general scalar robust optimization problems under the strictly robust counterpart are considered, among which, the uncertainties are included in the objective as well as the constraints. Besides, on the strength of a corrected image in a new type, an equivalent relation between the uncertain optimization problem and its image problem is also established, which provides an idea to tackle with minimax problems. Furthermore, theorems of the robust weak alternative as well as sufficient characterizations of robust optimality conditions are achieved on the frame of the linear and nonlinear (regular) weak separation functions. Moreover, several necessary and sufficient optimality conditions, especially saddle point sufficient optimality conditions for scalar robust optimization problems, are obtained. Finally, a simple example for finding a shortest path is included to show the effectiveness of the results derived in this paper.

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Acknowledgements

The authors gratefully thank the anonymous referees and Professor F. Giannessi for their constructive suggestions and comments, which helped to improve the paper. Also thanks to Manxue You (Chongqing University) for helpful discussions on the image space analysis.

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Authors and Affiliations

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

    Hong-Zhi Wei, 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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Corresponding author

Correspondence to Chun-Rong Chen.

Additional information

This research was supported by the National Natural Science Foundation of China (Grant Numbers: 11301567 and 11571055) and the Fundamental Research Funds for the Central Universities (Grant Number: 106112015CDJXY100002).

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Wei, HZ., Chen, CR. & Li, SJ. Characterizations for Optimality Conditions of General Robust Optimization Problems. J Optim Theory Appl 177, 835–856 (2018). https://doi.org/10.1007/s10957-018-1256-y

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  • DOI: https://doi.org/10.1007/s10957-018-1256-y

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