Peaceman-Rachford Splitting Method Converges Ergodically for Solving Convex Optimization Problems
Optimization and Control
2025-01-15 v1
Abstract
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.
Cite
@article{arxiv.2501.07807,
title = {Peaceman-Rachford Splitting Method Converges Ergodically for Solving Convex Optimization Problems},
author = {Kaihuang Chen and Defeng Sun and Yancheng Yuan and Guojun Zhang and Xinyuan Zhao},
journal= {arXiv preprint arXiv:2501.07807},
year = {2025}
}