cuPDLPx: A GPU-Accelerated First-Order LP Solver

cuPDLPx is a GPU-accelerated linear programming solver based on a restarted Halpern PDHG method specifically tailored for GPU architectures. It incorporates a Halpern update scheme, an adaptive restart scheme, and a PID-controlled primal weight, resulting in substantial empirical improvements over its predecessor, cuPDLP, on standard LP benchmark suites.

cuPDLPx solves linear programs of the form

$$\begin{aligned} \min_{x} \quad & c^\top x \\\ \text{s.t.} \quad & \ell_c \le Ax \le u_c, \\\ & \ell_v \le x \le u_v. \end{aligned}$$

Our work is presented in two papers:

• Computational Paper: cuPDLPx: A Further Enhanced GPU-Based First-Order Solver for Linear Programming details the practical innovations that give cuPDLPx its performance edge.

• Theoretical Paper: Restarted Halpern PDHG for Linear Programming provides the mathematical foundation for our method.

For installation instructions, examples, solver parameters, and algorithm details, see the cuPDLPx documentation.

Interfaces

Interface	Description
Command line	Solve MPS files from a shell.
Python	Build and solve LPs with NumPy and SciPy.
Julia	Use cuPDLPx through JuMP and MathOptInterface.
C	Embed cuPDLPx in native applications.

References

If you use cuPDLPx or the ideas in your work, please cite the source below.

@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}
}

@article{lu2024restarted,
  title={Restarted Halpern PDHG for linear programming},
  author={Lu, Haihao and Yang, Jinwen},
  journal={arXiv preprint arXiv:2407.16144},
  year={2024}
}

License

cuPDLPx is licensed under the Apache 2.0 License. See the LICENSE file for details.