Radius of Robust Feasibility of System of Convex Inequalities with Uncertain Data

  • Jiawei Chen
  • Jun Li
  • Xiaobing Li
  • Yibing Lv
  • Jen-Chih YaoEmail author
Technical Note


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.


System of uncertain convex inequalities Radius of robust feasibility Minkowski function 

Mathematics Subject Classification

49J53 65K10 90C29 



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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Jiawei Chen
    • 1
  • Jun Li
    • 1
  • Xiaobing Li
    • 2
  • Yibing Lv
    • 3
  • Jen-Chih Yao
    • 4
    Email author
  1. 1.School of Mathematics and StatisticsSouthwest UniversityChongqingChina
  2. 2.College of Mathematics and StatisticsChongqing Jiaotong UniversityChongqingChina
  3. 3.School of Information and MathematicsYangtze UniversityJingzhouChina
  4. 4.Research Center for Interneural Computing, China Medical University HospitalChina Medical UniversityTaichungTaiwan

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