# cuPDLP.jl: A GPU Implementation of Restarted Primal-Dual Hybrid Gradient for Linear Programming in Julia

arXiv: https://arxiv.org/abs/2311.12180 · HTML: https://mlsanity.com/paper/2311.12180/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2023.

## Built on by (most cited first, 8 of 8)

- [MPAX: Mathematical Programming in JAX](https://mlsanity.com/paper/2412.09734/) (2024)
- [Nonlinear Optimization with GPU-Accelerated Neural Network Constraints](https://mlsanity.com/paper/2509.22462/) (2025)
- [Batched First-Order Methods for Parallel LP Solving in MIP](https://mlsanity.com/paper/2601.21990/) (2026)
- [TSENOR: Highly-Efficient Algorithm for Finding Transposable N:M Sparse Masks](https://mlsanity.com/paper/2505.23949/) (2025)
- [Parameter Tuning with Generalization Guarantees for GPU-Accelerated Linear Programming](https://mlsanity.com/paper/2606.08638/) (2026)
- [SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling](https://mlsanity.com/paper/2607.00095/) (2026)
- [GPU-Enabled Large-Scale Optimization Using Randomized Linear Algebra](https://mlsanity.com/paper/2609.08136/) (2026)
- [Reinforcement Learning to Accelerate Primal-Dual Hybrid Gradient for Linear Programming](https://mlsanity.com/paper/2610.01546/) (2026)

## Abstract (arXiv)

In this paper, we provide an affirmative answer to the long-standing question: Are GPUs useful in solving linear programming? We present cuPDLP.jl, a GPU implementation of restarted primal-dual hybrid gradient (PDHG) for solving linear programming (LP). We show that this prototype implementation in Julia has comparable numerical performance on standard LP benchmark sets to Gurobi, a highly optimized implementation of the simplex and interior-point methods. This demonstrates the power of using GPUs in linear programming, which, for the first time, showcases that GPUs and first-order methods can lead to performance comparable to state-of-the-art commercial optimization LP solvers on standard benchmark sets.