A Newton-Like Dynamical System for Nonsmooth and Nonconvex Optimization
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929619970555904 |
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| author | Garrido, Juan Guillermo Pérez-Aros, Pedro Vilches, Emilio |
| author_facet | Garrido, Juan Guillermo Pérez-Aros, Pedro Vilches, Emilio |
| contents | This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The classical Newton method's second-order information is extended by incorporating the graphical derivative of a locally Lipschitz mapping. Specifically, we analyze the existence and uniqueness of solutions, along with the asymptotic behavior of the system's trajectories. Conditions for convergence and respective convergence rates are established under two distinct scenarios: strong metric subregularity and satisfaction of the Kurdyka-Lojasiewicz inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Newton-Like Dynamical System for Nonsmooth and Nonconvex Optimization Garrido, Juan Guillermo Pérez-Aros, Pedro Vilches, Emilio Optimization and Control This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The classical Newton method's second-order information is extended by incorporating the graphical derivative of a locally Lipschitz mapping. Specifically, we analyze the existence and uniqueness of solutions, along with the asymptotic behavior of the system's trajectories. Conditions for convergence and respective convergence rates are established under two distinct scenarios: strong metric subregularity and satisfaction of the Kurdyka-Lojasiewicz inequality. |
| title | A Newton-Like Dynamical System for Nonsmooth and Nonconvex Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2412.05952 |