An Augmented Lagrangian Approach to Composite Problems with a Random Linear Operator
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929607864745984 |
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| author | Greenstein, Dan Hallak, Nadav |
| author_facet | Greenstein, Dan Hallak, Nadav |
| contents | We consider the minimization of a sum of a smooth function with a nonsmooth composite function, where the composition is applied on a random linear mapping. This random composite model encompasses many problems, and can especially capture realistic scenarios in which the data is sampled during the optimization process. We propose and analyze a method that combines the classical Augmented Lagrangian framework with a sampling mechanism and adaptive update of the penalty parameter. We show that every accumulation point of the sequence produced by our algorithm is almost surely a critical point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01055 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Augmented Lagrangian Approach to Composite Problems with a Random Linear Operator Greenstein, Dan Hallak, Nadav Optimization and Control We consider the minimization of a sum of a smooth function with a nonsmooth composite function, where the composition is applied on a random linear mapping. This random composite model encompasses many problems, and can especially capture realistic scenarios in which the data is sampled during the optimization process. We propose and analyze a method that combines the classical Augmented Lagrangian framework with a sampling mechanism and adaptive update of the penalty parameter. We show that every accumulation point of the sequence produced by our algorithm is almost surely a critical point. |
| title | An Augmented Lagrangian Approach to Composite Problems with a Random Linear Operator |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2305.01055 |