dHPR: A Distributed Halpern Peaceman--Rachford Method for Non-smooth Distributed Optimization Problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914156070830080 |
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| author | Feng, Zhangcheng Sun, Defeng Yuan, Yancheng Zhang, Guojun |
| author_facet | Feng, Zhangcheng Sun, Defeng Yuan, Yancheng Zhang, Guojun |
| contents | This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$ iteration complexity regarding Karush--Kuhn--Tucker residual. By leveraging the symmetric Gauss--Seidel decomposition, the dHPR effectively decouples the linear operators in the objective functions and consensus constraints while maintaining parallelizability and avoiding additional large proximal terms, leading to a decentralized implementation with provably fast convergence. The superior performance of dHPR is demonstrated through comprehensive numerical experiments on distributed LASSO, group LASSO, and $L_1$-regularized logistic regression problems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_10069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | dHPR: A Distributed Halpern Peaceman--Rachford Method for Non-smooth Distributed Optimization Problems Feng, Zhangcheng Sun, Defeng Yuan, Yancheng Zhang, Guojun Optimization and Control Distributed, Parallel, and Cluster Computing Multiagent Systems This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$ iteration complexity regarding Karush--Kuhn--Tucker residual. By leveraging the symmetric Gauss--Seidel decomposition, the dHPR effectively decouples the linear operators in the objective functions and consensus constraints while maintaining parallelizability and avoiding additional large proximal terms, leading to a decentralized implementation with provably fast convergence. The superior performance of dHPR is demonstrated through comprehensive numerical experiments on distributed LASSO, group LASSO, and $L_1$-regularized logistic regression problems. |
| title | dHPR: A Distributed Halpern Peaceman--Rachford Method for Non-smooth Distributed Optimization Problems |
| topic | Optimization and Control Distributed, Parallel, and Cluster Computing Multiagent Systems |
| url | https://arxiv.org/abs/2511.10069 |