Calculus of sequential normal compactness in variational analysis

In this paper we study some properties of sets, set-valued mappings, and extended-real-valued functions unified under the name of “sequential normal compactness.” These properties automatically hold in finite-dimensional spaces, while they play a major role in infinite-dimensional variational analys...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 282; no. 1; pp. 63 - 84
Main Authors: Mordukhovich, Boris S., Wang, Bingwu
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.06.2003
Elsevier
Subjects:
Banach and Asplund spaces
Calculus rules
Exact sciences and technology
Extremal principle
Functional analysis
Generalized differentiation
Mathematical analysis
Mathematics
Sciences and techniques of general use
Sequential normal compactness
Variational analysis
Variational analysis
Extremal principle
Calculus rules
Generalized differentiation
Banach and Asplund spaces
Sequential normal compactness
Optimal control
Compactness
Optimality condition
Functional analysis
Differentiation
Banach space
Generalization
Constrained optimization
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:In this paper we study some properties of sets, set-valued mappings, and extended-real-valued functions unified under the name of “sequential normal compactness.” These properties automatically hold in finite-dimensional spaces, while they play a major role in infinite-dimensional variational analysis. In particular, they are essential for calculus rules involving generalized differential constructions, for stability and metric regularity results and their broad applications, for necessary optimality conditions in constrained optimization and optimal control, etc. This paper contains principal results ensuring the preservation of sequential normal compactness properties under various operations over sets, set-valued mappings, and functions.
ISSN:0022-247X
1096-0813
DOI:10.1016/S0022-247X(02)00385-2