A CONVEX REPRESENTATION OF MAXIMAL MONOTONE OPERATORS

By Juan Enrique Martínez-Legaz. 2003

95 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/bda7ccec344f6bb9d33fff2982ed8d96985b569b

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Citations in the corpus

Monotone Operators Representable by l.s.c. Convex Functions (2005, background): “In a recent paper, Mart́ınez-Legaz and Théra [8] rediscovered the Fitzpatrick function associated to maximal monotone operators and characterized the family {φA | A ⊂ X ×X∗ is maximal monotone} .”
Quantitative Stochastic Homogenization and Large-Scale Regularity (2017, background): “This variational formulation for non-self adjoint elliptic operators (as well as similar variational principles for parabolic equations, gradient flows and other problems) have been discovered and rediscovered multiple times, in the PDE community (see [28, 82]), by convex analysts [54, 86] and by nu”
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], Mart́inez-Legaz and Théra [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 spa”
MAXIMAL MONOTONICITY, CONJUGATION AND THE DUALITY PRODUCT (2003, background): “entials of saddle functions on X ×X. After that, Fitzpatrick [4] proved that maximal monotone operators can be represented by convex functions on X × X∗. This result has been recently rediscovered in [6, 2]. Next we describe Fitzpatrick’s results. Given a maximal monotone operator T : X ⇒X∗, deﬁne H”
A new proof for Rockafellar’s characterization of maximal monotone operators (2004, methodology): “2 using a characterization of maximal monotone subsets of X ×X∗ given by Martinez-Legaz and Théra in [4] and some properties of convex functions associated to monotone subsets from Penot [5], but the use of Lemma 1.”