FORWARD-BACKWARD SPLITTING WITH DEVIATIONS FOR MONOTONE INCLUSIONS
(2024) In Applied Set-Valued Analysis and Optimization 6(2). p.113-135- Abstract
We propose and study a weakly convergent variant of the forward-backward algorithm for solving structured monotone inclusion problems. Our algorithm features a per-iteration deviation vector, providing additional degrees of freedom. The only requirement on the deviation vector to guarantee convergence is that its norm is bounded by a quantity that can be computed online. This approach offers great flexibility and paves the way for the design of new forward-backward-based algorithms, while still retaining global convergence guarantees. These guarantees include linear convergence under a metric subregularity assumption. Choosing suitable monotone operators enables the incorporation of deviations into other algorithms, such as the... (More)
We propose and study a weakly convergent variant of the forward-backward algorithm for solving structured monotone inclusion problems. Our algorithm features a per-iteration deviation vector, providing additional degrees of freedom. The only requirement on the deviation vector to guarantee convergence is that its norm is bounded by a quantity that can be computed online. This approach offers great flexibility and paves the way for the design of new forward-backward-based algorithms, while still retaining global convergence guarantees. These guarantees include linear convergence under a metric subregularity assumption. Choosing suitable monotone operators enables the incorporation of deviations into other algorithms, such as the Chambolle-Pock method and Krasnosel'skii-Mann iterations. We propose a novel inertial primal-dual algorithm by selecting the deviations along a momentum direction and deciding their size by using the norm condition. Numerical experiments validate our convergence claims and demonstrate that even this simple choice of a deviation vector can enhance the performance compared to, for instance, the standard Chambolle-Pock algorithm. Copy: 2024 Applied Set-Valued Analysis and Optimization.
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- author
- Sadeghi, Hamed LU ; Banert, Sebastian LU and Giselsson, Pontus LU
- organization
- publishing date
- 2024-08-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Forward-backward splitting, Global convergence, Inertial primal-dual algorithm, Linear convergence rate, Monotone inclusions
- in
- Applied Set-Valued Analysis and Optimization
- volume
- 6
- issue
- 2
- pages
- 23 pages
- publisher
- Biemdas Academic Publishers
- external identifiers
-
- scopus:85189006469
- ISSN
- 2562-7775
- DOI
- 10.23952/asvao.6.2024.2.01
- language
- English
- LU publication?
- yes
- id
- 6d145755-a704-4e2c-a128-cb54cbf0d064
- date added to LUP
- 2024-04-16 15:40:06
- date last changed
- 2024-04-17 02:58:34
@article{6d145755-a704-4e2c-a128-cb54cbf0d064, abstract = {{<p>We propose and study a weakly convergent variant of the forward-backward algorithm for solving structured monotone inclusion problems. Our algorithm features a per-iteration deviation vector, providing additional degrees of freedom. The only requirement on the deviation vector to guarantee convergence is that its norm is bounded by a quantity that can be computed online. This approach offers great flexibility and paves the way for the design of new forward-backward-based algorithms, while still retaining global convergence guarantees. These guarantees include linear convergence under a metric subregularity assumption. Choosing suitable monotone operators enables the incorporation of deviations into other algorithms, such as the Chambolle-Pock method and Krasnosel'skii-Mann iterations. We propose a novel inertial primal-dual algorithm by selecting the deviations along a momentum direction and deciding their size by using the norm condition. Numerical experiments validate our convergence claims and demonstrate that even this simple choice of a deviation vector can enhance the performance compared to, for instance, the standard Chambolle-Pock algorithm. Copy: 2024 Applied Set-Valued Analysis and Optimization.</p>}}, author = {{Sadeghi, Hamed and Banert, Sebastian and Giselsson, Pontus}}, issn = {{2562-7775}}, keywords = {{Forward-backward splitting; Global convergence; Inertial primal-dual algorithm; Linear convergence rate; Monotone inclusions}}, language = {{eng}}, month = {{08}}, number = {{2}}, pages = {{113--135}}, publisher = {{Biemdas Academic Publishers}}, series = {{Applied Set-Valued Analysis and Optimization}}, title = {{FORWARD-BACKWARD SPLITTING WITH DEVIATIONS FOR MONOTONE INCLUSIONS}}, url = {{http://dx.doi.org/10.23952/asvao.6.2024.2.01}}, doi = {{10.23952/asvao.6.2024.2.01}}, volume = {{6}}, year = {{2024}}, }