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Citation

If you use cuPDLPx in published work, please cite the computational paper. If your work also relies on the restarted Halpern PDHG method or its convergence theory, please cite the theoretical paper as well.

Computational paper

Algorithmic enhancements, GPU implementation, and numerical results are described in this paper:

@article{lu2025cupdlpx,
  title   = {{cuPDLPx}: A Further Enhanced GPU-Based First-Order Solver
             for Linear Programming},
  author  = {Lu, Haihao and Peng, Zedong and Yang, Jinwen},
  journal = {arXiv preprint arXiv:2507.14051},
  year    = {2025},
  url     = {https://arxiv.org/abs/2507.14051}
}

Theoretical paper

Restarted Halpern PDHG and its reflected variant are developed in this paper:

@article{lu2024restarted,
  title   = {Restarted Halpern PDHG for Linear Programming},
  author  = {Lu, Haihao and Yang, Jinwen},
  journal = {arXiv preprint arXiv:2407.16144},
  year    = {2024},
  url     = {https://arxiv.org/abs/2407.16144}
}

Background

Papers

Blogs

Open-source solvers

  • cuPDLP.jl, the earlier Julia GPU solver.
  • cuPDLP-C, the C implementation of cuPDLP.
  • PDQP.jl, a Julia first-order solver for convex quadratic programming on CPUs and NVIDIA GPUs.
  • PDHCG, a GPU-accelerated first-order solver for convex quadratic and conic quadratic programming.
  • HPR-LP-C, a C GPU solver for LP based on the Halpern Peaceman–Rachford method.
  • cuOpt, NVIDIA's open-source GPU-accelerated optimization library for LP, MIP, and vehicle routing.
  • HiGHS, an open-source solver for LP, MIP, and QP that includes a PDLP-based first-order LP solver.
  • D-PDLP, a distributed LP solver built on cuPDLPx for execution across multiple GPUs.
  • CoolPDLP.jl, a Julia implementation of PDLP and its variants with support for CPUs, multiple GPU architectures, and batched solves.

Commercial solvers (implementing PDLP)

Benchmarks

Acknowledgements

The development of cuPDLPx is partially supported by AFOSR Grant No. FA9550-24-1-0051, ONR Grant No. N000142412735, and the NVIDIA Academic Grant Program.