This paper aims to understand the relationships among recently developed GPU-accelerated first-order methods (FOMs) for linear programming (LP), with particular emphasis on HPR-LP -- a Halpern Peaceman--Rachford (HPR) method for LP. Our findings can be summarized as follows: (i) the base algorithm of cuPDLPx, a recently released GPU solver, is a special case of the base algorithm of HPR-LP, thereby showing that cuPDLPx is another concrete implementation instance of HPR-LP; (ii) once the active sets have been identified, HPR-LP and EPR-LP -- an ergodic PR method for LP -- become equivalent under the same initialization; and (iii) extensive numerical experiments on benchmark datasets demonstrate that HPR-LP achieves the best overall performance among current GPU-accelerated LP solvers. These findings provide a strong motivation for using the HPR method as a baseline to further develop GPU-accelerated LP solvers and beyond.
@article{arxiv.2509.23903,
title = {On the Relationships among GPU-Accelerated First-Order Methods for Solving Linear Programming},
author = {Kaihuang Chen and Defeng Sun and Yancheng Yuan and Guojun Zhang and Xinyuan Zhao},
journal= {arXiv preprint arXiv:2509.23903},
year = {2025}
}
Comments
Compared to the previous version, we have added numerical comparisons with cuPDLPx