Comparison of Proximal First-Order Primal and Primal-Dual algorithms via Performance Estimation
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909137935269888 |
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| author | Bousselmi, Nizar Pustelnik, Nelly Hendrickx, Julien M. Glineur, François |
| author_facet | Bousselmi, Nizar Pustelnik, Nelly Hendrickx, Julien M. Glineur, François |
| contents | Selecting the fastest algorithm for a specific signal/image processing task is a challenging question. We propose an approach based on the Performance Estimation Problem framework that numerically and automatically computes the worst-case performance of a given optimization method on a class of functions. We first propose a computer-assisted analysis and comparison of several first-order primal optimization methods, namely, the gradient method, the forward-backward, Peaceman-Rachford, and Douglas-Rachford splittings. We tighten the existing convergence results of these algorithms and extend them to new classes of functions. Our analysis is then extended and evaluated in the context of the primal-dual Chambolle-Pock and Condat-Vũ methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10209 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comparison of Proximal First-Order Primal and Primal-Dual algorithms via Performance Estimation Bousselmi, Nizar Pustelnik, Nelly Hendrickx, Julien M. Glineur, François Optimization and Control Selecting the fastest algorithm for a specific signal/image processing task is a challenging question. We propose an approach based on the Performance Estimation Problem framework that numerically and automatically computes the worst-case performance of a given optimization method on a class of functions. We first propose a computer-assisted analysis and comparison of several first-order primal optimization methods, namely, the gradient method, the forward-backward, Peaceman-Rachford, and Douglas-Rachford splittings. We tighten the existing convergence results of these algorithms and extend them to new classes of functions. Our analysis is then extended and evaluated in the context of the primal-dual Chambolle-Pock and Condat-Vũ methods. |
| title | Comparison of Proximal First-Order Primal and Primal-Dual algorithms via Performance Estimation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2403.10209 |