{"ID":2842145,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.10069","arxiv_id":"2511.10069","title":"dHPR: A Distributed Halpern Peaceman--Rachford Method for Non-smooth Distributed Optimization Problems","abstract":"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.","short_abstract":"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 symmetri...","url_abs":"https://arxiv.org/abs/2511.10069","url_pdf":"https://arxiv.org/pdf/2511.10069v1","authors":"[\"Zhangcheng Feng\",\"Defeng Sun\",\"Yancheng Yuan\",\"Guojun Zhang\"]","published":"2025-11-13T08:15:26Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.DC\",\"cs.MA\"]","methods":"[]","has_code":false}