Inexact Gauss-Newton methods with matrix approximation by sampling for nonlinear least-squares and systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910731708923904 |
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| author | Bellavia, Stefania Malaspina, Greta Morini, Benedetta |
| author_facet | Bellavia, Stefania Malaspina, Greta Morini, Benedetta |
| contents | We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the deterministic models. The analysis of the expected number of iterations needed in the worst case to achieve a desired level of accuracy in the first-order optimality condition provides guidelines for applying sampling and enforcing, with \minor{a} fixed probability, a suitable accuracy in the random approximations. Results of the numerical validation of the algorithms are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_05501 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inexact Gauss-Newton methods with matrix approximation by sampling for nonlinear least-squares and systems Bellavia, Stefania Malaspina, Greta Morini, Benedetta Optimization and Control Numerical Analysis We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the deterministic models. The analysis of the expected number of iterations needed in the worst case to achieve a desired level of accuracy in the first-order optimality condition provides guidelines for applying sampling and enforcing, with \minor{a} fixed probability, a suitable accuracy in the random approximations. Results of the numerical validation of the algorithms are presented. |
| title | Inexact Gauss-Newton methods with matrix approximation by sampling for nonlinear least-squares and systems |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2310.05501 |