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

arXiv: https://arxiv.org/abs/2601.07628 · HTML: https://mlsanity.com/paper/2601.07628/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2026.

## Built on by (most cited first, 1 of 1)

- [GPU-Accelerated Bregman Douglas-Rachford Splitting for Discrete Optimal Transport](https://mlsanity.com/paper/2610.04715/) (2026)

## Abstract (arXiv)

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.