Monotone and nonmonotone linearized block coordinate descent methods for nonsmooth composite optimization problems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908407872618496 |
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| author | Nabou, Yassine Bourkhissi, Lahcen El Stich, Sebastian U. Valkonen, Tuomo |
| author_facet | Nabou, Yassine Bourkhissi, Lahcen El Stich, Sebastian U. Valkonen, Tuomo |
| contents | In this paper, we introduce both monotone and nonmonotone variants of LiBCoD, a \textbf{Li}nearized \textbf{B}lock \textbf{Co}ordinate \textbf{D}escent method for solving composite optimization problems. At each iteration, a random block is selected, and the smooth components of the objective are linearized along the chosen block in a Gauss-Newton approach. For the monotone variant, we establish a global sublinear convergence rate to a stationary point under the assumption of bounded iterates. For the nonmonotone variant, we derive a global sublinear convergence rate without requiring global Lipschitz continuity or bounded iterates. Preliminary numerical experiments highlight the promising performance of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12397 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monotone and nonmonotone linearized block coordinate descent methods for nonsmooth composite optimization problems Nabou, Yassine Bourkhissi, Lahcen El Stich, Sebastian U. Valkonen, Tuomo Optimization and Control In this paper, we introduce both monotone and nonmonotone variants of LiBCoD, a \textbf{Li}nearized \textbf{B}lock \textbf{Co}ordinate \textbf{D}escent method for solving composite optimization problems. At each iteration, a random block is selected, and the smooth components of the objective are linearized along the chosen block in a Gauss-Newton approach. For the monotone variant, we establish a global sublinear convergence rate to a stationary point under the assumption of bounded iterates. For the nonmonotone variant, we derive a global sublinear convergence rate without requiring global Lipschitz continuity or bounded iterates. Preliminary numerical experiments highlight the promising performance of the proposed approach. |
| title | Monotone and nonmonotone linearized block coordinate descent methods for nonsmooth composite optimization problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2506.12397 |