# cuPDLPx: A Further Enhanced GPU-Based First-Order Solver for Linear Programming

arXiv: https://arxiv.org/abs/2507.14051 · HTML: https://mlsanity.com/paper/2507.14051/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2025.

## Built on by (most cited first, 5 of 5)

- [Batched First-Order Methods for Parallel LP Solving in MIP](https://mlsanity.com/paper/2601.21990/) (2026)
- [Parameter Tuning with Generalization Guarantees for GPU-Accelerated Linear Programming](https://mlsanity.com/paper/2606.08638/) (2026)
- [Dual-guided Hierarchical Edge Localization for Large-scale Optimal Transport Across Dimensions](https://mlsanity.com/paper/2609.13010/) (2026)
- [Reinforcement Learning to Accelerate Primal-Dual Hybrid Gradient for Linear Programming](https://mlsanity.com/paper/2610.01546/) (2026)
- [GPU-Accelerated Bregman Douglas-Rachford Splitting for Discrete Optimal Transport](https://mlsanity.com/paper/2610.04715/) (2026)

## Abstract (arXiv)

We introduce cuPDLPx, a further enhanced GPU-based first-order solver for linear programming. Building on the recently developed restarted Halpern PDHG for LP, cuPDLPx incorporates a number of new techniques, including a new restart criterion and a PID-controlled primal weight update. These improvements are carefully tailored for GPU architectures and deliver substantial computational gains. Across benchmark datasets, cuPDLPx achieves 2.5x-5x speedups on MIPLIB LP relaxations and 3x-6.8x on Mittelmann's benchmark set, with particularly strong improvements in high-accuracy and presolve-enabled settings. The solver is publicly available at https://github.com/MIT-Lu-Lab/cuPDLPx.