Hölder Error Bounds and Hölder Calmness with Applications to Convex Semi-infinite Optimization

  • Alexander Y. KrugerEmail author
  • Marco A. López
  • Xiaoqi Yang
  • Jiangxing Zhu


Using techniques of variational analysis, necessary and sufficient subdifferential conditions for Hölder error bounds are investigated and some new estimates for the corresponding modulus are obtained. As an application, we consider the setting of convex semi-infinite optimization and give a characterization of the Hölder calmness of the argmin mapping in terms of the level set mapping (with respect to the objective function) and a special supremum function. We also estimate the Hölder calmness modulus of the argmin mapping in the framework of linear programming.


Hölder error bounds Hölder calmness Convex programming Semi-infinite programming 

Mathematics Subject Classification (2010)

49J53 90C25 90C31 90C34 


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The authors would like to thank Prof. Xi Yin Zheng for his valuable comments which helped us improve the presentation of the paper and Dr Li Minghua who has read the preliminary version of the manuscript and found a mistake in one of the proofs. We are grateful to PhD students Bui Thi Hoa and Nguyen Duy Cuong from Federation University Australia for carefully reading the manuscript, eliminating numerous glitches and contributing to Example 3.19.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Centre for Informatics and Applied Optimization, Federation University AustraliaBallaratAustralia
  2. 2.Department of MathematicsUniversity of AlicanteAlicanteSpain
  3. 3.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHung HomHong Kong
  4. 4.Department of MathematicsYunnan UniversityKunmingChina

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