Abstract
In this paper, we investigate the radius of robust feasibility of system of uncertain convex inequalities by the Minkowski function. We firstly establish an upper bound and a lower bound for radius of robust feasibility of the system of uncertain convex inequalities. Exact formulas of radius of robust feasibility of the system are derived under the nonsymmetric and symmetric assumptions of the uncertain sets. We also obtain a characterization on the positiveness of radius of robust feasibility for the system. Lastly, explicit tractable formulas for computing the radius of robust feasibility of the system are presented when the uncertain sets are ellipsoids, polytopes, boxes and unit ball, respectively.
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Acknowledgements
The authors would like to thank the associate editor and anonymous referees for their careful reading and pertinent suggestions, which have helped to improve the paper significantly. This research was partially supported by the MOST 108-2115-M-039-005-MY3, the Natural Science Foundation of China (11401487, 11771058, 11871383), the Hubei Provincial Natural Science Foundation for Distinguished Young Scholars (2019CFA088), the China Ministry of Education Humanities and Social Science Research Youth Fund and the Program of Chongqing Innovation Team Project in University (CXTDX201601022).
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Chen, J., Li, J., Li, X. et al. Radius of Robust Feasibility of System of Convex Inequalities with Uncertain Data . J Optim Theory Appl 184, 384–399 (2020). https://doi.org/10.1007/s10957-019-01607-7
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DOI: https://doi.org/10.1007/s10957-019-01607-7