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 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 -regularized logistic regression problems.
Cite
@article{arxiv.2511.10069,
title = {dHPR: A Distributed Halpern Peaceman--Rachford Method for Non-smooth Distributed Optimization Problems},
author = {Zhangcheng Feng and Defeng Sun and Yancheng Yuan and Guojun Zhang},
journal= {arXiv preprint arXiv:2511.10069},
year = {2025}
}