An accelerated randomized Bregman-Kaczmarz method for strongly convex linearly constraint optimization
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916671027937280 |
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| author | Tondji, Lionel Lorenz, Dirk A. Necoara, Ion |
| author_facet | Tondji, Lionel Lorenz, Dirk A. Necoara, Ion |
| contents | In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain acceleration we build on the fact that the Kaczmarz method is dual to a coordinate descent method. We use a recently proposed acceleration method for the randomized coordinate descent and transfer it to the primal space. This method inherits many of the attractive features of the accelerated coordinate descent method, including its worst-case convergence rates. A theoretical analysis of the convergence of the proposed method is given. Numerical experiments show that the proposed method is more efficient and faster than the existing methods for solving the same problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01160 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An accelerated randomized Bregman-Kaczmarz method for strongly convex linearly constraint optimization Tondji, Lionel Lorenz, Dirk A. Necoara, Ion Optimization and Control Numerical Analysis 65F10, 68W20, 90C25 In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain acceleration we build on the fact that the Kaczmarz method is dual to a coordinate descent method. We use a recently proposed acceleration method for the randomized coordinate descent and transfer it to the primal space. This method inherits many of the attractive features of the accelerated coordinate descent method, including its worst-case convergence rates. A theoretical analysis of the convergence of the proposed method is given. Numerical experiments show that the proposed method is more efficient and faster than the existing methods for solving the same problem. |
| title | An accelerated randomized Bregman-Kaczmarz method for strongly convex linearly constraint optimization |
| topic | Optimization and Control Numerical Analysis 65F10, 68W20, 90C25 |
| url | https://arxiv.org/abs/2504.01160 |