Calculus of directional subdifferentials and coderivatives in Banach spaces
Document Type
Article
Publication Date
2017
Department/School
Mathematics
Publication Title
Positivity
Abstract
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.
Link to Published Version
Recommended Citation
Long, P., Wang, B., & Yang, X. (2017). Calculus of directional subdifferentials and coderivatives in Banach spaces. Positivity, 21(1), 223–254. https://doi.org/10.1007/s11117-016-0417-1