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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Excesses, duality gaps and weak compactness


Author: Stephen Simons
Journal: Proc. Amer. Math. Soc. 130 (2002), 2941-2946
MSC (2000): Primary 46B10, 46N10, 49J35, 49N15
Published electronically: March 13, 2002
MathSciNet review: 1908917
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Abstract: We explore the connection between the concepts ``excess'' and ``duality gap'' from epigraphical analysis and optimization, and the functional analytic concepts of weak* and weak compactness. We also discuss briefly the connection with R. C. James's ``sup theorem''.


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Additional Information

Stephen Simons
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106-3080
Email: simons@math.ucsb.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06456-0
PII: S 0002-9939(02)06456-0
Keywords: Normed space, excess, minimax theorem, duality gap, weak--star and weak compactness
Received by editor(s): May 1, 2001
Published electronically: March 13, 2002
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2002 American Mathematical Society