The relevance of convex analysis for the study of monotonicity

By Jean-Paul Penot. 2004

126 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4e536f8ea09a3e04424d9c4294081e705c89dad1

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Convex Functions: Constructions, Characterizations and Counterexamples (2010, background): “On being rediscovered and exploited by [137, 343, 344] and then by many others the field was rejuvenated.”
A new proof for Rockafellar’s characterization of maximal monotone operators (2004, methodology): “It is possible to prove Theorem 1.2 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 1.1 leads to a much shorter proof.”
Some problems about the representation of monotone operators by convex functions (2005, methodology): “[15] J.-P. Penot, “Is convexity useful for the study of monotonicity?””
The kernel average for two convex functions and its application to the extension and representation of monotone operators (2009, methodology): “As in [14, 15, 16], we say that f is autoconjugate ⇔ fT = f∗;”
Maximality of sums of two maximal monotone operators in general Banach space (2007, methodology): “The argument, based on a conjugate formula of Penot [8, Prop.”
Lipschitz Regularity for Elliptic Equations with Random Coefficients (2014, methodology): “In the first step, we introduce a function F∞ on R ×Rd that can be thought of as an indicator function of the graph of a [36].”
Fitzpatrick functions, cyclic monotonicity and Rockafellar's antiderivative (2007, background): “3 was first observed by Penot [34] when X is reflexive.”