Calculus of directional coderivatives and normal cones in Asplund spaces

We study the directional Mordukhovich normal cones to nonsmooth sets, coderivatives of set-valued mappings in Asplund spaces and establish extensive calculus results on these constructions under various operations of sets and mappings. We also develop calculus of the directional sequential normal co...

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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. 3; pp. 1115 - 1142
Main Authors: Long, Pujun, Wang, Bingwu, Yang, Xinmin
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.09.2017
Springer Nature B.V
Subjects:
Calculus
Calculus of Variations and Optimal Control; Optimization
Cones
Econometrics
Fourier Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Potential Theory
Directional Mordukhovich coderivative
Variational analysis
49J53
49J52
Directional Mordukhovich normal cone
49J50
Strict differentiability
Directional sequential normal compactness
Generalized differential calculus
Directional differentiability
ISSN:1385-1292, 1572-9281
Online Access:Get full text
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Summary:We study the directional Mordukhovich normal cones to nonsmooth sets, coderivatives of set-valued mappings in Asplund spaces and establish extensive calculus results on these constructions under various operations of sets and mappings. We also develop calculus of the directional sequential normal compactness both in general Banach spaces and in Asplund spaces.
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ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-016-0455-8