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.

Installation

Requirements

• GPU: NVIDIA GPU with CUDA 12.4+.
• Build Tools: CMake (≥ 3.20), GCC, NVCC.

Build from Source

Clone the repository and compile the project using CMake.

git clone git@github.com:MIT-Lu-Lab/cuPDLPx.git
cd cuPDLPx
cmake -B build
cmake --build build --clean-first

This will create the solver binary at ./build/cupdlpx.

Verifying the Installation

Run a small test problem to confirm that the solver was built correctly.

# 1. Download a test instance from the MIPLIB library
wget -P test/ https://miplib.zib.de/WebData/instances/2club200v15p5scn.mps.gz

# 2. Solve the problem and write output to the current directory (.)
./build/cupdlpx test/2club200v15p5scn.mps.gz test/

If the solver runs and creates output files, your installation is successful.

Python Package Installation

To use cuPDLPx in Python, you can install the pre-built package cupdlpx directly from PyPI:

pip install cupdlpx

Or build from source:

git clone https://github.com/MIT-Lu-Lab/cuPDLPx.git
cd cuPDLPx
pip install .

Usage & Interfaces

Command-line Interface

After building the project, the ./build/cupdlpx binary can be invoked from the command line as follows:

./build/cupdlpx [OPTIONS] <mps_file> <output_directory>

Arguments

• <mps_file>: The path to the input linear programming problem. Both plain (.mps) and gzipped (.mps.gz) files are supported.
• <output_directory>: The directory where the output files will be saved.

Solver Options

Option	Type	Description	Default
-h, --help	flag	Display the help message.	N/A
-v, --verbose	flag	Enable verbose logging.	false
--time_limit	double	Time limit in seconds.	3600.0
--iter_limit	int	Iteration limit.	2147483647
--opt_norm	string	Norm for optimality criteria: l2 or linf	l2
--eps_opt	double	Relative optimality tolerance.	1e-4
--eps_feas	double	Relative feasibility tolerance.	1e-4
--l_inf_ruiz_iter	int	Iterations for L-inf Ruiz rescaling	10
--no_pock_chambolle	flag	Disable Pock-Chambolle rescaling	enabled
--pock_chambolle_alpha	float	Value for Pock-Chambolle alpha	1.0
--no_bound_obj_rescaling	flag	Disable bound objective rescaling	enabled
--eval_freq	int	Termination evaluation frequency	200
--sv_max_iter	int	Max iterations for singular value estimation	5000
--sv_tol	float	Tolerance for singular value estimation	1e-4
--no_presolve	flag	Disable presolve	enabled
-f,--feasibility_polishing	flag	Run the polishing loop	false
--eps_feas_polish	double	Relative tolerance for polishing	1e-6

Output Files

The solver generates three text files in the specified <output_directory>. The filenames are derived from the input file's basename. For an input INSTANCE.mps.gz, the output will be:

<output_directory>/
├── INSTANCE_summary.txt          # Statistics, timings, and termination status
├── INSTANCE_primal_solution.txt  # Primal solution vector
└── INSTANCE_dual_solution.txt    # Dual solution vector

Python Interface

The cupdlpx Python package supports building and solving LPs directly with NumPy and SciPy. Documentation and examples are available in the Python API Guide.

Julia Interface

CuPDLPx.jl provides a JuMP/MathOptInterface wrapper for cuPDLPx, enabling cuPDLPx to be used as a solver backend for JuMP models. Documentation and examples are available at: CuPDLPx.jl.

C Interface

The public C API is defined in header file include/cupdlpx.h. A detailed description with usage examples can be found in the C API Guide.

Reference

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.