A simple closure condition for the normal cone intersection formula

Authors:
Regina Sandra Burachik and Vaithilingam Jeyakumar

Journal:
Proc. Amer. Math. Soc. **133** (2005), 1741-1748

MSC (2000):
Primary 46N10, 90C25

DOI:
https://doi.org/10.1090/S0002-9939-04-07844-X

Published electronically:
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:
https://doi.org/10.1090/S0002-9939-04-07844-X

Keywords:
Normal cone,
closure condition,
bounded linear regularity,
convex optimization,
strong conical hull intersection property

Received by editor(s):
February 16, 2004

Published electronically:
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

Article copyright:
© Copyright 2004
American Mathematical Society