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A new proof of the integrability of the subdifferential of a convex function on a Banach space
Author(s):
Milen
Ivanov;
Nadia
Zlateva
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1787-1793.
MSC (2000):
Primary 52A41, 49J53;
Secondary 26E15, 47H05
Posted:
January 30, 2008
MathSciNet review:
2373609
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Additional information
Abstract:
We provide a simple proof of the Moreau-Rockafellar theorem that a proper lower semicontinuous convex function on a Banach space is determined up to a constant by its subdifferential.
References:
-
- 1.
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- 2.
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 -subgradients and maximal monotonicity, Pac. J. Math. 103 (1982), 307-314. MR 705231 (85h:90091) - 3.
- A. Brøndsted, R. T. Rockafellar, On the subdifferentiability of convex functions, Proc. Amer. Math. Soc. 16 (1965), 605-611. MR 0178103 (31:2361)
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- 6.
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- 7.
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- 8.
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- 9.
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- 11.
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Additional Information:
Milen
Ivanov
Affiliation:
Faculty of Mathematics and Informatics, University of Sofia, 5, James Bourchier Blvd., 1164 Sofia, Bulgaria
Email:
milen@fmi.uni-sofia.bg
Nadia
Zlateva
Affiliation:
Faculty of Mathematics and Informatics, University of Sofia, 5, James Bourchier Blvd., 1164 Sofia, Bulgaria
Email:
zlateva@fmi.uni-sofia.bg
DOI:
10.1090/S0002-9939-08-09178-8
PII:
S 0002-9939(08)09178-8
Keywords:
Convex function,
subdifferential
Received by editor(s):
January 8, 2007
Posted:
January 30, 2008
Additional Notes:
The first author was supported in part by the
Research and Development Fund of Sofia University,
Contract # 22/2006; and by NSFR of Bulgaria,
Contract # 401/2004.
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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