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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.03965 |
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| _version_ | 1866908393263857664 |
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| author | Bellavia, Stefania Malaspina, Greta Morini, Benedetta |
| author_facet | Bellavia, Stefania Malaspina, Greta Morini, Benedetta |
| contents | We present a stochastic inexact Gauss-Newton method for the solution of nonlinear least-squares. To reduce the computational cost with respect to the classical method, at each iteration the proposed algorithm approximately minimizes the local model on a random subspace. The dimension of the subspace varies along the iterations, and two strategies are considered for its update: the first is based solely on the Armijo condition, the latter is based on information from the true Gauss-Newton model. Under suitable assumptions on the objective function and the random subspace, we prove a probabilistic bound on the number of iterations needed to drive the norm of the gradient below any given threshold. Moreover, we provide a theoretical analysis of the local behavior of the method. The numerical experiments demonstrate the effectiveness of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A variable dimension sketching strategy for nonlinear least-squares Bellavia, Stefania Malaspina, Greta Morini, Benedetta Optimization and Control We present a stochastic inexact Gauss-Newton method for the solution of nonlinear least-squares. To reduce the computational cost with respect to the classical method, at each iteration the proposed algorithm approximately minimizes the local model on a random subspace. The dimension of the subspace varies along the iterations, and two strategies are considered for its update: the first is based solely on the Armijo condition, the latter is based on information from the true Gauss-Newton model. Under suitable assumptions on the objective function and the random subspace, we prove a probabilistic bound on the number of iterations needed to drive the norm of the gradient below any given threshold. Moreover, we provide a theoretical analysis of the local behavior of the method. The numerical experiments demonstrate the effectiveness of the proposed method. |
| title | A variable dimension sketching strategy for nonlinear least-squares |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2506.03965 |