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Norm-closure of the barrier cone in normed linear spaces
Author(s):
Samir
Adly;
Emil
Ernst;
Michel
Théra
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2911-2915.
MSC (2000):
Primary 46N10, 47N10
Posted:
May 12, 2004
MathSciNet review:
2063110
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Abstract:
The aim of this note is to characterize the norm-closure of the barrier cone of a closed convex set in an arbitrary normed linear space by means of a new geometric object, the temperate cone.
References:
- 1.
- J.-P. Aubin, Optima and Equilibria, An Introduction to Nonlinear Analysis, Graduate Texts in Mathematics, vol. 140, Springer-Verlag, Berlin, 1993. MR 94b:49002
- 2.
- D. Azé, Éléments d'Analyse Convexe et Variationnelle, Ellipse, 1997.
- 3.
- J. M. Borwein and J. D. Vanderwerff, Convergence of Lipschitz Regularizations of Convex Functions, J. Funct. Anal. 128, 139-162, 1995. MR 96m:49022
- 4.
- R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1968. MR 43:445
- 5.
- R. T. Rockafellar, Level Sets and Continuity of Conjugate Convex Functions, Trans. Amer. Math. Soc. 123, 46-63, 1966. MR 33:544
- 6.
- C. Zalinescu, Convex Analysis in General Vector Spaces, World Scientific, River Edge, NJ, 2002. MR 2003k:49003
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Additional Information:
Samir
Adly
Affiliation:
LACO, Université de Limoges, 123 Avenue A. Thomas, 87060 Limoges Cedex, France
Email:
adly@unilim.fr
Emil
Ernst
Affiliation:
Laboratoire de Modélisation en Mécanique et Thermodynamique (LMMT), Casse 322, Faculté de Sciences et Techniques de Saint Jérome, Avenue Escadrille Normandie-Niemen 13397 Marseille Cedex 20, France
Email:
Emil.Ernst@univ.u-3mrs.fr
Michel
Théra
Affiliation:
LACO, Université de Limoges, 123 Avenue A. Thomas, 87060 Limoges Cedex, France
Email:
michel.thera@unilim.fr
DOI:
10.1090/S0002-9939-04-07492-1
PII:
S 0002-9939(04)07492-1
Keywords:
Fenchel conjugate,
barrier cone,
temperate cone,
linearly bounded set,
recession cone
Received by editor(s):
July 15, 2002
Posted:
May 12, 2004
Additional Notes:
The third author's research was partially supported by the French Chilean Scientific Cooperation Programme ECOS under grant C00E05 and by NATO Collaborative Linkage Grant 978488.
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2004,
American Mathematical Society
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