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

TL;DR

This paper presents HPR-LP, a new solver for linear programming that leverages an HPR method with adaptive strategies, demonstrating significant speed improvements over existing solvers on benchmark datasets.

Contribution

Introduces an HPR-LP solver with adaptive restart and penalty updates, achieving faster convergence and robustness for linear programming problems.

Findings

Achieves 2.39x to 5.70x speedup over PDLP on benchmark datasets.

Demonstrates the effectiveness of adaptive strategies in HPR-LP.

Provides extensive numerical experiments validating performance.

Abstract

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 $\textbf{2.39x}$ to $\textbf{5.70x}$ speedup measured by SGM10 on benchmark datasets with presolve ($\textbf{2.03x}$ to $\textbf{4.06x}$ without presolve) over the award-winning solver PDLP with the tolerance of $10^{-8}$.