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Differential Stability of Convex Optimization Problems with Possibly Empty Solution Sets

  • Duong Thi Viet An
  • Jen-Chih YaoEmail author
Article
  • 152 Downloads

Abstract

This paper studies differential stability of infinite-dimensional convex optimization problems, whose solution sets may be empty. By using suitable sum rules for \(\varepsilon \)-subdifferentials, we obtain exact formulas for computing the \(\varepsilon \)-subdifferential of the optimal value function. Several illustrative examples are also given.

Keywords

Parametric convex programming Optimal value function Conjugate function \(\varepsilon \)-Subdifferentials \(\varepsilon \)-Normal directions 

Mathematics Subject Classification

49J53 49Q12 90C25 90C31 

Notes

Acknowledgements

The research of Duong Thi Viet An was supported by Thai Nguyen University of Sciences and the Vietnam Institute for Advanced Study in Mathematics (VIASM). The research of Jen-Chih Yao was supported by the Grant MOST 105-2221-E-039-009-MY3. The authors would like to thank Prof. Nguyen Dong Yen for useful comments and suggestions.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsThai Nguyen University of SciencesThai Nguyen CityVietnam
  2. 2.Center for General EducationChina Medical UniversityTaichungTaiwan

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