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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2402.02193 |
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| _version_ | 1866913947125284864 |
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| author | Liu, Zekun |
| author_facet | Liu, Zekun |
| contents | We consider a 3-block Alternating Direction Method of Multipliers (ADMM) for solving nonconvex nonseparable problems with a linear constraint. Inspired by \cite[Sun, Toh and Yang, \textit{SIAM Journal on Optimization}, 25 (2015), pp.882-915]{wtwice}, the proposed ADMM follows the Block Coordinate Descent (BCD) cycle order $1\to 3\to 2\to 3$. We analyze its convergence based on the Kurdyka-Łojasiewicz property. We also discuss two useful extensions of the proposed ADMM with $2\to 3\to 1\to 3$ Gauss-Seidel BCD cycle order, and with adding a proximal term for more general nonseparable problems, respectively. Moreover, we make numerical experiments on two nonconvex problems: robust principal component analysis and nonnegative matrix completion. Results show the efficiency and outperformance of the proposed ADMM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Extended ADMM for 3-Block Nonconvex Nonseparable Problems with Applications Liu, Zekun Optimization and Control Information Theory 65K10, 90C26, 90C90 We consider a 3-block Alternating Direction Method of Multipliers (ADMM) for solving nonconvex nonseparable problems with a linear constraint. Inspired by \cite[Sun, Toh and Yang, \textit{SIAM Journal on Optimization}, 25 (2015), pp.882-915]{wtwice}, the proposed ADMM follows the Block Coordinate Descent (BCD) cycle order $1\to 3\to 2\to 3$. We analyze its convergence based on the Kurdyka-Łojasiewicz property. We also discuss two useful extensions of the proposed ADMM with $2\to 3\to 1\to 3$ Gauss-Seidel BCD cycle order, and with adding a proximal term for more general nonseparable problems, respectively. Moreover, we make numerical experiments on two nonconvex problems: robust principal component analysis and nonnegative matrix completion. Results show the efficiency and outperformance of the proposed ADMM. |
| title | An Extended ADMM for 3-Block Nonconvex Nonseparable Problems with Applications |
| topic | Optimization and Control Information Theory 65K10, 90C26, 90C90 |
| url | https://arxiv.org/abs/2402.02193 |