A Linear Convergence Result for the Jacobi-Proximal Alternating Direction Method of Multipliers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917126288179200 |
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| author | Choi, Hyelin Choi, Woocheol |
| author_facet | Choi, Hyelin Choi, Woocheol |
| contents | In this paper, we analyze the convergence rate of the Jacobi-Proximal Alternating Direction Method of Multipliers (ADMM) initially introduced by Deng et al. for the block-structured optimization problem with linear constraint. The algorithm is well-suited for parallel implementation and widely used for large-scale multi-block optimization problems. While the o(1/k) convergence of the Jacobi-Proximal ADMM for the case $N \geq 3$ has been well-established in the previous work, to the best of our knowledge, its linear convergence for $N \geq 3$ remains unproven. We establish the linear convergence of the algorithm when the cost functions are strongly convex and smooth. Numerical experiments are presented supporting the convergence result. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_18601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Linear Convergence Result for the Jacobi-Proximal Alternating Direction Method of Multipliers Choi, Hyelin Choi, Woocheol Optimization and Control 90C25 G.1.6 In this paper, we analyze the convergence rate of the Jacobi-Proximal Alternating Direction Method of Multipliers (ADMM) initially introduced by Deng et al. for the block-structured optimization problem with linear constraint. The algorithm is well-suited for parallel implementation and widely used for large-scale multi-block optimization problems. While the o(1/k) convergence of the Jacobi-Proximal ADMM for the case $N \geq 3$ has been well-established in the previous work, to the best of our knowledge, its linear convergence for $N \geq 3$ remains unproven. We establish the linear convergence of the algorithm when the cost functions are strongly convex and smooth. Numerical experiments are presented supporting the convergence result. |
| title | A Linear Convergence Result for the Jacobi-Proximal Alternating Direction Method of Multipliers |
| topic | Optimization and Control 90C25 G.1.6 |
| url | https://arxiv.org/abs/2503.18601 |