A simple closure condition for the normal cone intersection formula

In this paper it is shown that if C and D are two closed convex subsets of a Banach space X and x\in C\cap D, then N_{C\cap D}(x)=N_{C}(x)+N_{D}(x) whenever the convex cone, \left(\mathrm{Epi} \sigma _{C}+\mathrm{Epi}\sigma _{D}\right), is weak* closed, where \sigma _{C} and N_{C} are the support fu...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2005-06, Vol.133 (6), p.1741-1748
Main Authors: Burachik, Regina Sandra, Vaithilingam Jeyakumar
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Banach space
College mathematics
Euclidean space
Exact sciences and technology
Functional analysis
Hilbert spaces
Mathematical analysis
Mathematical functions
Mathematical programming
Mathematics
Operational research and scientific management
Operational research. Management science
Sciences and techniques of general use
Topological regularity
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Summary:In this paper it is shown that if C and D are two closed convex subsets of a Banach space X and x\in C\cap D, then N_{C\cap D}(x)=N_{C}(x)+N_{D}(x) whenever the convex cone, \left(\mathrm{Epi} \sigma _{C}+\mathrm{Epi}\sigma _{D}\right), is weak* closed, where \sigma _{C} and N_{C} are the support function and the normal cone of the set C respectively. This closure condition is shown to be weaker than the standard interior-point-like conditions and the bounded linear regularity condition.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-04-07844-X