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A simple closure condition for the normal cone intersection formula
Author(s):
Regina
Sandra
Burachik;
Vaithilingam
Jeyakumar
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1741-1748.
MSC (2000):
Primary 46N10, 90C25
Posted:
December 21, 2004
MathSciNet review:
2120273
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Abstract:
In this paper it is shown that if  and  are two closed convex subsets of a Banach space  and  , then  whenever the convex cone,  , is weak* closed, where  and  are the support function and the normal cone of the set  respectively. This closure condition is shown to be weaker than the standard interior-point-like conditions and the bounded linear regularity condition.
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Additional Information:
Regina
Sandra
Burachik
Affiliation:
Engenharia de Sistemas e Computacao, COPPE-UFRJ CP 68511, Rio de Janeiro-RJ, CEP 21945-970, Brazil
Email:
regi@cos.ufrj.br
Vaithilingam
Jeyakumar
Affiliation:
Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia
Email:
jeya@maths.unsw.edu.au
DOI:
10.1090/S0002-9939-04-07844-X
PII:
S 0002-9939(04)07844-X
Keywords:
Normal cone,
closure condition,
bounded linear regularity,
convex optimization,
strong conical hull intersection property
Received by editor(s):
February 16, 2004
Posted:
December 21, 2004
Additional Notes:
The first author's research was supported by CAPES (Grant BEX 0664-02/2), and was partially completed while the author was a visitor at the School of Mathematics, University of New South Wales, Sydney, and the School of Mathematics and Statistics, University of South Australia. This author wishes to thank the School of Mathematics at the University of South Australia for providing a stimulating environment and good infrastructure during her longer stay there, and also to the School of Mathematics at the University of New South Wales for their support. The authors are thankful to Jonathan Borwein for his helpful suggestions and for referring us to paper [4] and to the referee for the careful reading of the manuscript.
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2004,
American Mathematical Society
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