Calculus of directional subdifferentials and coderivatives in Banach spaces

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 con...

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 21; no. 1; pp. 223 - 254
Main Authors: Long, Pujun, Wang, Bingwu, Yang, Xinmin
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.03.2017
Springer Nature B.V
Subjects:
Banach spaces
Calculus
Calculus of Variations and Optimal Control; Optimization
Econometrics
Fourier Analysis
Mathematical analysis
Mathematical functions
Mathematics
Mathematics and Statistics
Operator Theory
Optimization
Potential Theory
Studies
Directional Mordukhovich coderivative
Variational analysis
Directional Mordukhovich subdifferential
49J53
49J52
Directional Mordukhovich normal cone
49J50
Strict differentiability
Generalized differential calculus
Marginal function
Directional differentiability
ISSN:1385-1292, 1572-9281
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-016-0417-1