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Positivity

pp 1–13 | Cite as

Sigma-subdifferential and its application to minimization problem

  • Hui HuangEmail author
  • Chunyou Sun
Article

Abstract

In this paper, we study \(\sigma \)-subdifferentials of \(\sigma \)-convex functions. Two equivalent conditions for \(\sigma \)-convexity are given. The formula for the \(\sigma \)-subdifferential of a sum of two functions is established. In terms of \(\sigma \)-subdifferential and Clarke’s normal cone, some Fermat’s rules for minimization problems are obtained.

Keywords

\(\sigma \)-Convex function \(\sigma \)-Subdifferential Fermat’s rule Banach space 

Mathematics Subject Classification

49J52 90C26 

Notes

Acknowledgements

The authors are greatly indebted to the reviewers and the Editor for their valuable comments. Huang’s research was supported by the National Natural Science Foundation of China (Grant No. 11461080). Sun’s research was supported by the National Natural Science Foundation of China (Grant Nos. 11522109 and 11871169).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsYunnan UniversityKunmingPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China

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