# HPR-LP: An implementation of an HPR method for solving linear programming

arXiv: https://arxiv.org/abs/2408.12179 · HTML: https://mlsanity.com/paper/2408.12179/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2024.

## Built on by (most cited first, 3 of 3)

- [MPAX: Mathematical Programming in JAX](https://mlsanity.com/paper/2412.09734/) (2024)
- [Batched First-Order Methods for Parallel LP Solving in MIP](https://mlsanity.com/paper/2601.21990/) (2026)
- [Dual-guided Hierarchical Edge Localization for Large-scale Optimal Transport Across Dimensions](https://mlsanity.com/paper/2609.13010/) (2026)

## Abstract (arXiv)

In this paper, we introduce an HPR-LP solver, an implementation of a Halpern Peaceman-Rachford (HPR) method with semi-proximal terms for solving linear programming (LP). The HPR method enjoys the iteration complexity of O(1/k) in terms of the Karush-Kuhn-Tucker residual and the objective error. Based on the complexity results, we design an adaptive strategy of restart and penalty parameter update to improve the efficiency and robustness of the HPR method. We conduct extensive numerical experiments on different LP benchmark datasets using NVIDIA A100-SXM4-80GB GPU in different stopping tolerances. Our solver's Julia version achieves a 2.39x to 5.70x speedup measured by SGM10 on benchmark datasets with presolve (2.03x to 4.06x without presolve) over the award-winning solver PDLP with the tolerance of 10-8.