Compositions and convex combinations of averaged nonexpansive operators
By Patrick L. Combettes, Isao Yamada. 2014
114 citations recorded by the source corpus.
Abstract Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward–backward splitting algorithm for finding a zero of the sum of two monotone operators is obtained.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/a6a0386183acc01b3857c3be320291e3d6765fc9
How researchers see this paper
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In Computational Theory and Mathematics
- Damek Davis
- Laurent Condat
- Jean-Christophe Pesquet
- Peter Richtárik
- Patrick L. Combettes
- Wotao Yin
- Stephen P. Boyd
- Ming Yan
In Geometry and Topology
- Laurent Condat
- Jean-Christophe Pesquet
- Stephen P. Boyd
- Damek Davis
- Peter Richtárik
- Ernest K. Ryu
- Pontus Giselsson
- Dmitry Kovalev
In Numerical Analysis
- Damek Davis
- Peter Richtárik
- Laurent Condat
- Patrick L. Combettes
- Jean-Christophe Pesquet
- Grigory Malinovsky
- Dmitry Kovalev
- Ming Yan
Citations in the corpus
- Plug-and-Play Methods Provably Converge with Properly Trained Denoisers (2019, unknown): “An mapping Lemma 5 ((Ogura & Yamada, 2002; Combettes & Yamada, 2015)) .”
- From Local SGD to Local Fixed Point Methods for Federated Learning (2020, methodology): “Fixed-point methods are typically made from compositions and averages of gradient or proximity operators of functions (Combettes & Yamada, 2015; Bauschke & Combettes, 2017); for instance, a sum of proximity operators corresponds to the ‘proximal average’ of functions (Yu, 2013).”
- SMART: The Stochastic Monotone Aggregated Root-Finding Algorithm (2016, background): “Proposition B.1 (Cocoercivness from Averagedness) Let α ∈ [0, 1], and let T : H → H be an α-averaged operator.”
- Stochastic Approximations and Perturbations in Forward-Backward Splitting for Monotone Operators (2015, background): “Recent theoretical advances on deterministic versions of this algorithm can be found in [6, 11, 20, 22].”
- Tight global linear convergence rate bounds for Douglas–Rachford splitting (2015, result): “Our result extends these results in that it allows also for negatively averaged operators and reduces to the result in [7] for averaged operators.”
- A Primer on Monotone Operator Methods (2015, background): “Interested readers can find a proof in [33,37].”