Recent Developments in HPR Methods for Large-Scale Linear Programming

@misc{chen2026recent,
  title = {{Recent Developments in HPR Methods for Large-Scale Linear Programming}},
  author = {Kaihuang Chen and Qilin Lai and Yijia Liang and Jiawei Lu and Defeng Sun and Yancheng Yuan and Guojun Zhang and Xiangyu Zhang and Xinyuan Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01872},
  eprint = {2611.01872},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01872},
}

TY  - UNPB
TI  - Recent Developments in HPR Methods for Large-Scale Linear Programming
AU  - Kaihuang Chen
AU  - Qilin Lai
AU  - Yijia Liang
AU  - Jiawei Lu
AU  - Defeng Sun
AU  - Yancheng Yuan
AU  - Guojun Zhang
AU  - Xiangyu Zhang
AU  - Xinyuan Zhao
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01872
UR  - https://arxiv.org/abs/2611.01872
AB  - We present recent developments in Halpern Peaceman-Rachford (HPR) methods for solving large-scale linear programming problems. We first introduce the semi-proximal HPR framework and summarize its convergence guarantees, together with its connections to Halpern PDHG and ergodic Peaceman-Rachford iterations. To improve practical performance, we develop adaptive restart and penalty parameter update strategies. We then describe several computational enhancements, including GPU-based preprocessing, diagonal scaling, reusable execution plans for sparse matrix-vector multiplication, and sieving techniques. We further discuss multi-GPU parallelization and lossless model storage and loading for handling large-scale instances. These developments form the foundation of HPR-LP, a GPU-accelerated solver for large-scale linear programming.
ER  -