Scaling Decision Optimization to 100 Million Variables and Beyond with mPDLP in NVIDIA cuOpt | NVIDIA Technical Blog

This post introduces the NVIDIA cuOpt Multi-GPU Primal-Dual hybrid gradient for Linear Programming (mPDLP) solver. It details how mPDLP distributes LP problems across NVLink-connected GPUs, reducing solve time for large problems and achieving up to 6x lower peak memory usage per GPU compared to single-GPU PDLP. The post explains the PDLP algorithm, the challenges of distributing it (communication overhead and load imbalance), and introduces min-cut partitioning as an improvement over 2D partitioning by exploiting shared dependencies between consecutive Sparse Matrix-Vector Multiplications (SpMVs). Benchmarking results and partner applications (Kinaxis, PSR) are presented to demonstrate the performance gains.