A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectives
In this short note, we provide a simple version of an accelerated forward-backward method (a.k.a. Nesterov’s accelerated proximal gradient method) possibly relying on approximate proximal operators and allowing to exploit strong convexity of the objective function. The method supports both relative...
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| Format: | Article |
| Language: | English |
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Université de Montpellier
2022-01-01
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| Series: | Open Journal of Mathematical Optimization |
| Online Access: | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.12/ |
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| _version_ | 1825205026769862656 |
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| author | Barré, Mathieu Taylor, Adrien Bach, Francis |
| author_facet | Barré, Mathieu Taylor, Adrien Bach, Francis |
| author_sort | Barré, Mathieu |
| collection | DOAJ |
| description | In this short note, we provide a simple version of an accelerated forward-backward method (a.k.a. Nesterov’s accelerated proximal gradient method) possibly relying on approximate proximal operators and allowing to exploit strong convexity of the objective function. The method supports both relative and absolute errors, and its behavior is illustrated on a set of standard numerical experiments.Using the same developments, we further provide a version of the accelerated proximal hybrid extragradient method of [21] possibly exploiting strong convexity of the objective function. |
| format | Article |
| id | doaj-art-ccfc9776096a4ae888de30c224f3ef60 |
| institution | Kabale University |
| issn | 2777-5860 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Université de Montpellier |
| record_format | Article |
| series | Open Journal of Mathematical Optimization |
| spelling | doaj-art-ccfc9776096a4ae888de30c224f3ef602025-02-07T14:02:43ZengUniversité de MontpellierOpen Journal of Mathematical Optimization2777-58602022-01-01311510.5802/ojmo.1210.5802/ojmo.12A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectivesBarré, Mathieu0Taylor, Adrien1Bach, Francis2INRIA (Sierra project-team) – Dépt. d’informatique, Ecole normale supérieure, CNRS, PSL Research University, Paris, FranceINRIA (Sierra project-team) – Dépt. d’informatique, Ecole normale supérieure, CNRS, PSL Research University, Paris, FranceINRIA (Sierra project-team) – Dépt. d’informatique, Ecole normale supérieure, CNRS, PSL Research University, Paris, FranceIn this short note, we provide a simple version of an accelerated forward-backward method (a.k.a. Nesterov’s accelerated proximal gradient method) possibly relying on approximate proximal operators and allowing to exploit strong convexity of the objective function. The method supports both relative and absolute errors, and its behavior is illustrated on a set of standard numerical experiments.Using the same developments, we further provide a version of the accelerated proximal hybrid extragradient method of [21] possibly exploiting strong convexity of the objective function.https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.12/ |
| spellingShingle | Barré, Mathieu Taylor, Adrien Bach, Francis A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectives Open Journal of Mathematical Optimization |
| title | A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectives |
| title_full | A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectives |
| title_fullStr | A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectives |
| title_full_unstemmed | A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectives |
| title_short | A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectives |
| title_sort | note on approximate accelerated forward backward methods with absolute and relative errors and possibly strongly convex objectives |
| url | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.12/ |
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