D-PDLP: Scaling PDLP to Distributed Multi-GPU Systems

Abstract

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.