Firmly Nonexpansive Mappings and Maximally Monotone Operators: Correspondence and Duality
By Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang. 2011
65 citations recorded by the source corpus.
The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximally monotone operators due to Minty. In this paper, we systematically analyze the relationship between properties of firmly nonexpansive mappings and associated maximally monotone operators. Dual and self-dual properties are also identified. The results are illustrated through several examples.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/f4a1516c1eb981d4cc7e393d4bd37a92540c3873
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
- Antonin Chambolle
- Thomas Pock
- Genaro López-Acedo
- David Ariza-Ruiz
- Laurentiu Leustean
- Marc Pollefeys
- Christian Häne
- Yekini Shehu
In Geometry and Topology
- Genaro López-Acedo
- David Ariza-Ruiz
- Antonin Chambolle
- Thomas Pock
- Laurentiu Leustean
- Ulrich Kohlenbach
In Numerical Analysis
- Thomas Pock
- Antonin Chambolle
- Genaro López-Acedo
- David Ariza-Ruiz
- Laurentiu Leustean
- Marc Pollefeys
- Christian Häne
- Stephen P. Boyd
Citations in the corpus
- Firmly nonexpansive mappings in classes of geodesic spaces (2012, background): “We refer to [2] for a very nice presentation of this correspondence.”
- An introduction to continuous optimization for imaging (2016, background): “The special case θ ≥ 1/2 is the case of ‘firmly non-expansive operators’, which is well known to coincide with the proximity operators and the resolvent (I +A)−1 of maximal-monotone operators (see the review in Bauschke et al. 2012).”