MAXIMAL MONOTONICITY, CONJUGATION AND THE DUALITY PRODUCT
By Regina Sandra Burachik, Benar Fux Svaiter. 2003
113 citations recorded by the source corpus.
Recently, the authors studied the connection between each maximal monotone operator T and a family H(T) 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/f640b2df1c1cad6ef6baf2731330dc6146ed39c6
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Xianfu Wang
- Jonathan Michael Borwein
- Heinz H. Bauschke
- Constantin Zᾰlinescu
- Jean-Paul Penot
- Simeon Reich
- Patrick L. Combettes
- Ernö Robert Csetnek
In Computational Theory and Mathematics
- Jonathan Michael Borwein
- Heinz H. Bauschke
- Simeon Reich
- Xianfu Wang
- Constantin Zᾰlinescu
- Jean-Paul Penot
- Sedi Bartz
- Patrick L. Combettes
Citations in the corpus
- Fitzpatrick functions, cyclic monotonicity and Rockafellar's antiderivative (2007, background): “Therefore, by [ 18, Theorem 3.1 ] (see also [45, Theorem 1.4] and [34, Theorem 6]), the set � (x,x�) 2 X × X� | FA,n(x,x�) = hx,x�i � is the graph of a maximal monotone operator.”
- Some problems about the representation of monotone operators by convex functions (2005, background): “[5] Representation of monotone operators by convex functions 5”
- The relevance of convex analysis for the study of monotonicity (2004, methodology): “The representation theorems of Fitzpatrick [15], Krauss [16]-[19], and their supplements by Burachik and Svaiter [ 9 ], Mart´inez-Legaz and Th´era [21] give some hopes to pass from results about convex functions to results about maximal monotone operators from a reflexive Banach space X to its dual ”
- Maximality of sums of two maximal monotone operators in general Banach space (2007, methodology): “For any monotone mapping T , we associate the Fitzpatrick function introduced by Simon Fitzpatrick in [6] but then neglected for many years until re-popularized in papers by Penot [8], Burachik-Svaiter [5], and others.”