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.
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The work of X. Yang was partially supported by the National Natural Science Foundation of China, Grant No.11431004.
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Long, P., Wang, B. & Yang, X. Calculus of directional subdifferentials and coderivatives in Banach spaces. Positivity 21, 223–254 (2017). https://doi.org/10.1007/s11117-016-0417-1
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DOI: https://doi.org/10.1007/s11117-016-0417-1
Keywords
- Variational analysis
- Directional Mordukhovich subdifferential
- Directional Mordukhovich normal cone
- Directional Mordukhovich coderivative
- Generalized differential calculus
- Marginal function
- Directional differentiability
- Strict differentiability