Adaptive Randomized Extended Bregman-Kaczmarz Method for Combined Optimization Problems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914258723274752 |
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| author | Dong, Zeyu Xiao, Aqin Yin, Guojian Yin, Junfeng |
| author_facet | Dong, Zeyu Xiao, Aqin Yin, Guojian Yin, Junfeng |
| contents | Combined optimization problems that couple data-fidelity and regularization terms arise naturally in a wide range of inverse problems. In this paper, we study an adaptive randomized averaging block extended Bregman-Kaczmarz (aRABEBK) method for solving such problems. The proposed method incorporates iteration-wise relaxation parameters that are automatically adjusted using residual information, allowing for more aggressive step sizes without additional manual tuning. We establish a convergence theory for the proposed framework and derive expected linear convergence rate guarantees. Numerical experiments on both synthetic and real data sets for sparse and minimum-norm least-squares problems demonstrate that our aRABEBK method achieves faster convergence and improved robustness compared with state-of-the-art extended Kaczmarz and Bregman-Kaczmarz-type algorithms, including its nonadaptive counterpart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11157 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive Randomized Extended Bregman-Kaczmarz Method for Combined Optimization Problems Dong, Zeyu Xiao, Aqin Yin, Guojian Yin, Junfeng Numerical Analysis Combined optimization problems that couple data-fidelity and regularization terms arise naturally in a wide range of inverse problems. In this paper, we study an adaptive randomized averaging block extended Bregman-Kaczmarz (aRABEBK) method for solving such problems. The proposed method incorporates iteration-wise relaxation parameters that are automatically adjusted using residual information, allowing for more aggressive step sizes without additional manual tuning. We establish a convergence theory for the proposed framework and derive expected linear convergence rate guarantees. Numerical experiments on both synthetic and real data sets for sparse and minimum-norm least-squares problems demonstrate that our aRABEBK method achieves faster convergence and improved robustness compared with state-of-the-art extended Kaczmarz and Bregman-Kaczmarz-type algorithms, including its nonadaptive counterpart. |
| title | Adaptive Randomized Extended Bregman-Kaczmarz Method for Combined Optimization Problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.11157 |