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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2601.11826 |
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| _version_ | 1866914260694597632 |
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| author | Lee, Young-Ju Park, Jongho |
| author_facet | Lee, Young-Ju Park, Jongho |
| contents | We propose a high-order version of the augmented Lagrangian method for solving convex optimization problems with linear constraints, which achieves arbitrarily fast -- and even superlinear -- convergence rates. First, we analyze the convergence rates of the high-order proximal point method under certain uniform convexity assumptions on the energy functional. We then introduce the high-order augmented Lagrangian method and analyze its convergence by leveraging the convergence results of the high-order proximal point method. Finally, we present applications of the high-order augmented Lagrangian method to various problems arising in the sciences, including data fitting, flow in porous media, and scientific machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11826 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A high-order augmented Lagrangian method with arbitrarily fast convergence Lee, Young-Ju Park, Jongho Optimization and Control 90C25, 90C46 We propose a high-order version of the augmented Lagrangian method for solving convex optimization problems with linear constraints, which achieves arbitrarily fast -- and even superlinear -- convergence rates. First, we analyze the convergence rates of the high-order proximal point method under certain uniform convexity assumptions on the energy functional. We then introduce the high-order augmented Lagrangian method and analyze its convergence by leveraging the convergence results of the high-order proximal point method. Finally, we present applications of the high-order augmented Lagrangian method to various problems arising in the sciences, including data fitting, flow in porous media, and scientific machine learning. |
| title | A high-order augmented Lagrangian method with arbitrarily fast convergence |
| topic | Optimization and Control 90C25, 90C46 |
| url | https://arxiv.org/abs/2601.11826 |