Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer_journal/representative-functions-of-maximally-monotone-operators-and-9VaqEsx0iu
References (24)
-
M. Alizadeh, N. Hadjisavvas (2013)
On the Fitzpatrick transform of a monotone bifunctionOptimization, 62
-
S. Fitzpatrick (1988)
Representing monotone operators by convex functions -
R. Burachik, B. Svaiter (2002)
Maximal Monotone Operators, Convex Functions and a Special Family of EnlargementsSet-Valued Analysis, 10
-
M. Alizadeh, N. Hadjisavvas (2012)
Local boundedness of monotone bifunctionsJournal of Global Optimization, 53
-
R. Boț, S. Grad (2011)
Approaching the maximal monotonicity of bifunctions via representative functionsarXiv: Optimization and Control
-
S. Simons (2006)
Dualized and scaled Fitzpatrick functions, 134
-
E Krauss (1985)
A representation of maximal monotone operators by saddle functionsRev. Roumaine Math. Pures Appl., 30
-
A. Iusem (2010)
On the Maximal Monotonicity of Diagonal Subdifferential Operators, 1281
-
S. Reich, S. Simons (2005)
Fenchel duality, Fitzpatrick functions and the Kirszbraun-Valentine extension theorem, 133
-
J. Borwein (2006)
Maximal Monotonicity via Convex Analysis -
R. Rockafellar (1971)
Saddle-points and convex analysis -
R. Rockafellar (1970)
On the virtual convexity of the domain and range of a nonlinear maximal monotone operatorMathematische Annalen, 185
-
RT Rockafellar (1971)
Differential Games and Related Topics -
N. Hadjisavvas, H. Khatibzadeh (2010)
Maximal monotonicity of bifunctionsOptimization, 59
-
E. Krauss (1985)
A representation of arbitrary maximal monotone operators via subgradients of skew-symmetric saddle functionsNonlinear Analysis-theory Methods & Applications, 9
-
R. Rockafellar (1966)
LEVEL SETS AND CONTINUITY OF CONJUGATE CONVEX FUNCTIONSTransactions of the American Mathematical Society, 123
-
S Simons, C Zalinescu (2005)
Fenchel duality, Fitzpatrick functions and maximal monotonicityJ. Nonlinear Convex Anal., 6
-
M. Alves, B. Svaiter, E. Castorina (2012)
A New Qualification Condition for the Maximality of the Sum of Maximal Monotone Operators in General Banach Spaces -
J. Martínez-Legaz, B. Svaiter (2005)
Monotone Operators Representable by l.s.c. Convex FunctionsSet-Valued Analysis, 13
-
R. Rockafellar, R. Rockafellar (1970)
On the maximal monotonicity of subdifferential mappings.Pacific Journal of Mathematics, 33
-
R. Rockafellar (1969)
Local boundedness of nonlinear, monotone operators.Michigan Mathematical Journal, 16
-
N. Hadjisavvas, F. Jacinto, J. Martínez-Legaz (2016)
Some Conditions for Maximal Monotonicity of BifunctionsSet-Valued and Variational Analysis, 24
-
C. Zălinescu (2002)
Convex analysis in general vector spaces -
RT Rockafellar (1970)
Convex Analysis. Princeton Mathematics
- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Mathematics of Computing; Numerical Analysis; Combinatorics; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics
- ISSN
- 0025-5610
- eISSN
- 1436-4646
- DOI
- 10.1007/s10107-016-1020-8
- Publisher site
- See Article on Publisher Site
Abstract
The aim of this paper is to show that every representative function of a maximally monotone operator is the Fitzpatrick transform of a bifunction corresponding to the operator. In fact, for each representative function $$\varphi $$ φ of the operator, there is a family of equivalent saddle functions (i.e., bifunctions which are concave in the first and convex in the second argument) each of which has $$\varphi $$ φ as Fitzpatrick transform. In the special case where $$\varphi $$ φ is the Fitzpatrick function of the operator, the family of equivalent saddle functions is explicitly constructed. In this way we exhibit the relation between the recent theory of representative functions, and the much older theory of saddle functions initiated by Rockafellar.
Journal
Mathematical Programming – Springer Journals
Published: May 11, 2016