Peaceman-Rachford Splitting Method Converges Ergodically for Solving Convex Optimization Problems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916565830598656 |
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| author | Chen, Kaihuang Sun, Defeng Yuan, Yancheng Zhang, Guojun Zhao, Xinyuan |
| author_facet | Chen, Kaihuang Sun, Defeng Yuan, Yancheng Zhang, Guojun Zhao, Xinyuan |
| contents | In this paper, we prove that the ergodic sequence generated by the Peaceman-Rachford (PR) splitting method with semi-proximal terms converges for convex optimization problems (COPs). Numerical experiments on the linear programming benchmark dataset further demonstrate that, with a restart strategy, the ergodic sequence of the PR splitting method with semi-proximal terms consistently outperforms both the point-wise and ergodic sequences of the Douglas-Rachford (DR) splitting method. These findings indicate that the restarted ergodic PR splitting method is a more effective choice for tackling large-scale COPs compared to its DR counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Peaceman-Rachford Splitting Method Converges Ergodically for Solving Convex Optimization Problems Chen, Kaihuang Sun, Defeng Yuan, Yancheng Zhang, Guojun Zhao, Xinyuan Optimization and Control 90C05, 90C06, 90C25 In this paper, we prove that the ergodic sequence generated by the Peaceman-Rachford (PR) splitting method with semi-proximal terms converges for convex optimization problems (COPs). Numerical experiments on the linear programming benchmark dataset further demonstrate that, with a restart strategy, the ergodic sequence of the PR splitting method with semi-proximal terms consistently outperforms both the point-wise and ergodic sequences of the Douglas-Rachford (DR) splitting method. These findings indicate that the restarted ergodic PR splitting method is a more effective choice for tackling large-scale COPs compared to its DR counterparts. |
| title | Peaceman-Rachford Splitting Method Converges Ergodically for Solving Convex Optimization Problems |
| topic | Optimization and Control 90C05, 90C06, 90C25 |
| url | https://arxiv.org/abs/2501.07807 |