An Inexact Proximal Newton Method for Nonconvex Composite Minimization
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913625432653824 |
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| author | Zhu, Hong |
| author_facet | Zhu, Hong |
| contents | In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and the local superlinear convergence rate in terms of the sequence generated by the proposed algorithm under the higher-order metric $q$-subregularity property. When the Lipschitz constant of the corresponding gradient is known, we show that the proposed algorithm is well-defined without line search. Extensive numerical experiments on the $\ell_1$-regularized Student's $t$-regression and the group penalized Student's $t$-regression show that the performance of the proposed method is comparable to the state-of-the-art proximal Newton-type methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_16535 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Inexact Proximal Newton Method for Nonconvex Composite Minimization Zhu, Hong Optimization and Control 90C26 49M15 65K05 In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and the local superlinear convergence rate in terms of the sequence generated by the proposed algorithm under the higher-order metric $q$-subregularity property. When the Lipschitz constant of the corresponding gradient is known, we show that the proposed algorithm is well-defined without line search. Extensive numerical experiments on the $\ell_1$-regularized Student's $t$-regression and the group penalized Student's $t$-regression show that the performance of the proposed method is comparable to the state-of-the-art proximal Newton-type methods. |
| title | An Inexact Proximal Newton Method for Nonconvex Composite Minimization |
| topic | Optimization and Control 90C26 49M15 65K05 |
| url | https://arxiv.org/abs/2412.16535 |