, Volume 21, Issue 1, pp 223–254 | Cite as

Calculus of directional subdifferentials and coderivatives in Banach spaces

  • Pujun Long
  • Bingwu Wang
  • Xinmin Yang


In this work we study the directional versions of Mordukhovich normal cones to nonsmooth sets, coderivatives of set-valued mappings, and subdifferentials of extended-real-valued functions in the framework of general Banach spaces. We establish some characterizations and basic properties of these constructions, and then develop calculus including sum rules and chain rules involving smooth functions. As an application, we also explore the upper estimates of the directional Mordukhovich subdifferentials and singular subdifferentials of marginal functions.


Variational analysis Directional Mordukhovich subdifferential Directional Mordukhovich normal cone Directional Mordukhovich coderivative Generalized differential calculus Marginal function Directional differentiability Strict differentiability 

Mathematics Subject Classification

49J53 49J50 49J52 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesInner Mongolia UniversityHohhotPeople’s Republic of China
  2. 2.Department of MathematicsEastern Michigan UniversityYpsilantiUSA
  3. 3.College of Mathematical SciencesChongqing Normal UniversityChongqingPeople’s Republic of China

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