Variable metric forward–backward splitting with applications to monotone inclusions in duality
By Patrick L. Combettes, Bang Công Vu. 2012
215 citations recorded by the source corpus.
We propose a variable metric forward–backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in duality. Some of these algorithms are new even when specialized to the fixed metric case. Various applications are discussed.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/02e359dbf1a32a8d507372a010bd1b8ecdbf8beb
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In Computational Theory and Mathematics
- Antonin Chambolle
- Thomas Pock
- Akira Hirabayashi
- Daichi Kitahara
- Andres A Contreras Marcillo
- Laurent Condat
- Ming Yan
- Marc Pollefeys
In Geometry and Topology
- Antonin Chambolle
- Laurent Condat
- Thomas Pock
- Akira Hirabayashi
- Daichi Kitahara
- Andres A Contreras Marcillo
In Numerical Analysis
- Thomas Pock
- Antonin Chambolle
- Akira Hirabayashi
- Daichi Kitahara
- Andres A Contreras Marcillo
- Laurent Condat
- Ming Yan
- Marc Pollefeys
Citations in the corpus
- Proximal Splitting Algorithms: A Tour of Recent Advances, with New Twists. (2020, background): “Moreover, there are many avenues for extensions, including the use of variable stepsizes or metrics [22,52], the study of convergence rates and development of accelerated variants [104–108], or the design of randomized versions [109–113].”
- An introduction to continuous optimization for imaging (2016, methodology): “S. Becker and J. Fadili (2012), A quasi-Newton proximal splitting method.”