Incremental Gauss--Newton Methods with Superlinear Convergence Rates
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929408544079872 |
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| author | Zhou, Zhiling Liu, Zhuanghua Liu, Chengchang Luo, Luo |
| author_facet | Zhou, Zhiling Liu, Zhuanghua Liu, Chengchang Luo, Luo |
| contents | This paper addresses the challenge of solving large-scale nonlinear equations with Hölder continuous Jacobians. We introduce a novel Incremental Gauss--Newton (IGN) method within explicit superlinear convergence rate, which outperforms existing methods that only achieve linear convergence rate. In particular, we formulate our problem by the nonlinear least squares with finite-sum structure, and our method incrementally iterates with the information of one component in each round. We also provide a mini-batch extension to our IGN method that obtains an even faster superlinear convergence rate. Furthermore, we conduct numerical experiments to show the advantages of the proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03195 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Incremental Gauss--Newton Methods with Superlinear Convergence Rates Zhou, Zhiling Liu, Zhuanghua Liu, Chengchang Luo, Luo Optimization and Control Machine Learning This paper addresses the challenge of solving large-scale nonlinear equations with Hölder continuous Jacobians. We introduce a novel Incremental Gauss--Newton (IGN) method within explicit superlinear convergence rate, which outperforms existing methods that only achieve linear convergence rate. In particular, we formulate our problem by the nonlinear least squares with finite-sum structure, and our method incrementally iterates with the information of one component in each round. We also provide a mini-batch extension to our IGN method that obtains an even faster superlinear convergence rate. Furthermore, we conduct numerical experiments to show the advantages of the proposed methods. |
| title | Incremental Gauss--Newton Methods with Superlinear Convergence Rates |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2407.03195 |