Extensions of generalized differential calculus in Asplund spaces

We develop an extended generalized differential calculus for normal cones to nonconvex sets, coderivatives of set-valued mappings, and subdifferential of extended-real-valued functions in infinite dimensions. This is a major area of modern variational analysis important for many applications, partic...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 272; no. 1; pp. 164 - 186
Main Authors: Mordukhovich, Boris S., Wang, Bingwu
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.08.2002
Elsevier
Subjects:
Exact sciences and technology
Manifolds and cell complexes
Mathematics
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Cone
Codimension subspace
Asplund space
Extreme value
Normal cone
Compactness
Subdifferential
Variational calculus
Reliability
Fréchet normal
Differentiation (calculus)
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:We develop an extended generalized differential calculus for normal cones to nonconvex sets, coderivatives of set-valued mappings, and subdifferential of extended-real-valued functions in infinite dimensions. This is a major area of modern variational analysis important for many applications, particularly to optimization, sensitivity, and control. We develop a unified geometric approach to the generalized differential calculus and obtain new results in this direction in a broad setting of Asplund spaces.
ISSN:0022-247X
1096-0813
DOI:10.1016/S0022-247X(02)00149-X