A Stochastic Iteratively Regularized Gauss-Newton Method
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912034081210368 |
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| author | Bergou, El Houcine Chada, Neil K. Diouane, Youssef |
| author_facet | Bergou, El Houcine Chada, Neil K. Diouane, Youssef |
| contents | This work focuses on developing and motivating a stochastic version of a wellknown inverse problem methodology. Specifically, we consider the iteratively regularized Gauss-Newton method, originally proposed by Bakushinskii for infinite-dimensional problems. Recent work have extended this method to handle sequential observations, rather than a single instance of the data, demonstrating notable improvements in reconstruction accuracy. In this paper, we further extend these methods to a stochastic framework through mini-batching, introducing a new algorithm, the stochastic iteratively regularized Gauss-Newton method (SIRGNM). Our algorithm is designed through the use randomized sketching. We provide an analysis for the SIRGNM, which includes a preliminary error decomposition and a convergence analysis, related to the residuals. We provide numerical experiments on a 2D elliptic PDE example. This illustrates the effectiveness of the SIRGNM, through maintaining a similar level of accuracy while reducing on the computational time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Stochastic Iteratively Regularized Gauss-Newton Method Bergou, El Houcine Chada, Neil K. Diouane, Youssef Numerical Analysis Optimization and Control 65N21, 65C35, 65K10, 93E24 This work focuses on developing and motivating a stochastic version of a wellknown inverse problem methodology. Specifically, we consider the iteratively regularized Gauss-Newton method, originally proposed by Bakushinskii for infinite-dimensional problems. Recent work have extended this method to handle sequential observations, rather than a single instance of the data, demonstrating notable improvements in reconstruction accuracy. In this paper, we further extend these methods to a stochastic framework through mini-batching, introducing a new algorithm, the stochastic iteratively regularized Gauss-Newton method (SIRGNM). Our algorithm is designed through the use randomized sketching. We provide an analysis for the SIRGNM, which includes a preliminary error decomposition and a convergence analysis, related to the residuals. We provide numerical experiments on a 2D elliptic PDE example. This illustrates the effectiveness of the SIRGNM, through maintaining a similar level of accuracy while reducing on the computational time. |
| title | A Stochastic Iteratively Regularized Gauss-Newton Method |
| topic | Numerical Analysis Optimization and Control 65N21, 65C35, 65K10, 93E24 |
| url | https://arxiv.org/abs/2409.12381 |