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Maximal monotonicity, conjugation and the duality product
Author(s):
Regina
Sandra
Burachik;
B.
F.
Svaiter
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2379-2383.
MSC (2000):
Primary 47H05
Posted:
March 18, 2003
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Abstract:
Recently, the authors studied the connection between each maximal monotone operator  and a family  of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities. The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular inequalities is associated to a unique maximal monotone operator.
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Additional Information:
Regina
Sandra
Burachik
Affiliation:
Engenharia de Sistemas e Computação, COPPE--UFRJ CP 68511, Rio de Janeiro--RJ, CEP 21945--970 Brazil
Email:
regi@cos.ufrj.br
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/S0002-9939-03-07053-9
PII:
S 0002-9939(03)07053-9
Keywords:
Convex functions,
maximal monotone operators,
duality product,
conjugation
Received by editor(s):
February 28, 2002
Posted:
March 18, 2003
Additional Notes:
The first author was partially supported by CNPq and by PRONEX--Optimization
The second author 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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