dHPR: A Distributed Halpern Peaceman--Rachford Method for Non-smooth Distributed Optimization Problems

Zhangcheng Feng, Defeng Sun, Yancheng Yuan, Guojun Zhang
11/13/2025
math.OCcs.DCcs.MA

No confident code implementation found for this paper.

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.

View on arXivView PDF

Code Implementations

No confident code match yet

We couldn't find an author-owned or strongly-evidenced community implementation for this paper. Any repos shown below are weak matches — verify before relying on them.

No code implementations found yet.

Know of an implementation? Let us know in the comments below!

Similar Papers

Fast Composite Optimization and Statistical Recovery in Federated Learning

85% match1 repo82022

Non-Ergodic Convergence Algorithms for Distributed Consensus and Coupling-Constrained Optimization

82% match2025

L1-Regularized Distributed Optimization: A Communication-Efficient Primal-Dual Framework

82% match1 repo372015

A cutting-surface consensus approach for distributed robust optimization of multi-agent systems

82% match2023

Learning (With) Distributed Optimization

82% match2023

2Direction: Theoretically Faster Distributed Training with Bidirectional Communication Compression

81% match2023

Cite this paper

@article{feng2025dhpr,
  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},
  year   = {2025},
  eprint = {2511.10069},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2511.10069v1}
}

Add a badge to your README

Shows whether official code is linked for this paper.

Code of Paper badge
[![Code of Paper](https://codeofpaper.com/badge/2511.10069.svg)](https://codeofpaper.com/paper/2511.10069)

Discussion