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Fixed points in the family of convex representations of a maximal monotone operator
Author(s):
B.
F.
Svaiter
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3851-3859.
MSC (2000):
Primary 47H05
Posted:
May 5, 2003
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Abstract:
Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exists a convex representation of the operator which is a fixed point of this conjugation.
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Additional Information:
B.
F.
Svaiter
Affiliation:
IMPA Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro--RJ, CEP 22460-320 Brazil
Email:
benar@impa.br
DOI:
10.1090/S0002-9939-03-07083-7
PII:
S 0002-9939(03)07083-7
Keywords:
Maximal monotone operators,
conjugation,
convex functions
Received by editor(s):
July 31, 2002
Posted:
May 5, 2003
Additional Notes:
This work was partially supported by CNPq Grant 301200/93-9(RN) and by PRONEX--Optimization
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2003,
American Mathematical Society
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