We present a distributed framework of the Primal-Dual Hybrid Gradient (PDHG) algorithm for solving massive-scale linear programming (LP) problems. Although PDHG-based solvers demonstrate strong performance on single-node GPU architectures, their applicability to industrial-scale instances is often limited by single-GPU computational throughput. To overcome these challenges, we propose D-PDLP, the first Distributed PDLP framework, which extends PDHG to a multi-GPU setting via a practical two-dimensional grid partitioning of the constraint matrix. To improve load balance and computational efficiency, we introduce a block-wise random permutation strategy combined with nonzero-aware matrix partitioning. By distributing the intensive computation required in PDHG iterations, the proposed framework harnesses multi-GPU parallelism to achieve substantial speedups with relatively low communication overhead. Extensive experiments on standard LP benchmarks (including MIPLIB and Mittelmann instances) as well as huge-scale real-world datasets show that our distributed implementation, built upon cuPDLPx, achieves strong scalability and high performance while preserving full FP64 numerical accuracy.

翻译：我们提出了一种基于原始-对偶混合梯度（PDHG）算法的分布式框架，用于求解大规模线性规划（LP）问题。尽管基于PDHG的求解器在单节点GPU架构上展现出强大性能，但其在工业级实例中的应用常受限于单GPU的计算吞吐量。为克服这些挑战，我们提出了首个分布式PDLP框架D-PDLP，通过将约束矩阵进行实用的二维网格划分，将PDHG扩展到多GPU环境。为提升负载均衡与计算效率，我们引入了一种结合非零感知矩阵划分的块式随机排列策略。通过分布PDHG迭代中的密集计算任务，所提框架利用多GPU并行性实现了大幅加速，且通信开销相对较低。在标准LP基准测试（包括MIPLIB和Mittelmann实例）及大规模真实世界数据集上的广泛实验表明，基于cuPDLPx构建的分布式实现，在保持完全FP64数值精度的同时，实现了强可扩展性与高性能。