Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918060954222592 |
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| author | Oikonomidis, Konstantinos Quan, Jan Laude, Emanuel Patrinos, Panagiotis |
| author_facet | Oikonomidis, Konstantinos Quan, Jan Laude, Emanuel Patrinos, Panagiotis |
| contents | We analyze nonlinearly preconditioned gradient methods for solving smooth minimization problems. We introduce a generalized smoothness property, based on the notion of abstract convexity, that is broader than Lipschitz smoothness and provide sufficient first- and second-order conditions. Notably, our framework encapsulates algorithms associated with the gradient clipping method and brings out novel insights for the class of $(L_0,L_1)$-smooth functions that has received widespread interest recently, thus allowing us to extend beyond already established methods. We investigate the convergence of the proposed method in both the convex and nonconvex setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness Oikonomidis, Konstantinos Quan, Jan Laude, Emanuel Patrinos, Panagiotis Optimization and Control We analyze nonlinearly preconditioned gradient methods for solving smooth minimization problems. We introduce a generalized smoothness property, based on the notion of abstract convexity, that is broader than Lipschitz smoothness and provide sufficient first- and second-order conditions. Notably, our framework encapsulates algorithms associated with the gradient clipping method and brings out novel insights for the class of $(L_0,L_1)$-smooth functions that has received widespread interest recently, thus allowing us to extend beyond already established methods. We investigate the convergence of the proposed method in both the convex and nonconvex setting. |
| title | Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2502.08532 |