Extensions of generalized differential calculus in Asplund spaces
type: Item
instance of: scholarly article
title: Extensions of generalized differential calculus in Asplund spaces
zbMATH Open document ID: 1006.49007
DOI: 10.1016/S0022-247X(02)00149-X
author: Boris S. Mordukhovich
author: Bingwu Wang
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-11-28T00:00:00Z
review text: The authors give an extended generalized differential calculus for nonconvex normal cones to sets, coderivatives of set-valued mappings and subdifferentials of extended real-valued functions in infinite-dimensional vector spaces, especially in Asplund spaces. Based on different versions of the extremal principle, a fuzzy intersection rule for the Fréchet normal cone and especially an intersection rule for the limiting normal cones to sets in product spaces (with respect to different topologies on the duals) are established. As a consequence one gets a representation of the limiting normal cones to inverse images of set-valued mappings. In the second part, these results are used for the derivation of sum rules and chain rules for the limiting coderivatives of set-valued mappings and for the limiting subdifferentials of real-valued functions.
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 49J53
Mathematics Subject Classification ID: 26E15
zbMATH DE Number: 1836783
zbMATH Keywords: generalized differential calculus
zbMATH Keywords: normal cones
zbMATH Keywords: coderivatives
zbMATH Keywords: set-valued mappings
zbMATH Keywords: subdifferentials
zbMATH Keywords: Asplund spaces
reviewed by: Jörg Thierfelder
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00149-x
OpenAlex ID: W1965316024
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description: scientific article; zbMATH DE number 1836783