Multilevel Bregman Proximal Gradient Descent
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913089765507072 |
|---|---|
| author | Elshiaty, Yara Petra, Stefania |
| author_facet | Elshiaty, Yara Petra, Stefania |
| contents | We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical multilevel optimization framework (MGOPT) to handle Bregman-based geometries and constrained domains. We provide a rigorous analysis of ML BPGD for multiple coarse levels and establish a global linear convergence rate. We demonstrate the effectiveness of ML BPGD in the context of image reconstruction, providing theoretical guarantees for the well-posedness of the multilevel framework and validating its performance through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03950 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multilevel Bregman Proximal Gradient Descent Elshiaty, Yara Petra, Stefania Optimization and Control 68U10, 65K10, 49M37 We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical multilevel optimization framework (MGOPT) to handle Bregman-based geometries and constrained domains. We provide a rigorous analysis of ML BPGD for multiple coarse levels and establish a global linear convergence rate. We demonstrate the effectiveness of ML BPGD in the context of image reconstruction, providing theoretical guarantees for the well-posedness of the multilevel framework and validating its performance through numerical experiments. |
| title | Multilevel Bregman Proximal Gradient Descent |
| topic | Optimization and Control 68U10, 65K10, 49M37 |
| url | https://arxiv.org/abs/2506.03950 |