|
Excesses, duality gaps and weak compactness
Author(s):
Stephen
Simons
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2941-2946.
MSC (2000):
Primary 46B10, 46N10, 49J35, 49N15
Posted:
March 13, 2002
MathSciNet review:
1908917
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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''.
References:
-
- 1.
- G. Beer, Topologies on closed and closed convex sets, Mathematics and Its Applications 268 (1993). MR 95k:49001
- 2.
- K. Fan, Minimax theorems, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 42-47. MR 14:1109f
- 3.
- S. Simons, Maximinimax, minimax, and antiminimax theorems and a result of R. C. James, Pac. J. Math. 40 (1972), 709-718. MR 47:756
- 4.
- -, Minimax and monotonicity, Lecture Notes in Mathematics 1693 (1998). MR 2001h:49002
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
46B10, 46N10, 49J35, 49N15
Retrieve articles in all Journals with
MSC (2000):
46B10, 46N10, 49J35, 49N15
Additional Information:
Stephen
Simons
Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106-3080
Email:
simons@math.ucsb.edu
DOI:
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
Posted:
March 13, 2002
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2002,
American Mathematical Society
|
