D-PDLP: A First-Order LP Solver Accelerated on Multiple GPUs

D-PDLP (Distributed PDLP) is a high-performance, distributed implementation of the Primal-Dual Hybrid Gradient (PDHG) algorithm designed for solving massive-scale Linear Programming (LP) problems on multi-GPU systems.

By leveraging 2D Grid Partitioning, D-PDLP scales the first-order PDHG method across GPU clusters, efficiently harnessing the aggregate computational power and memory of multiple devices. This implementation is built upon cuPDLPx, a GPU-accelerated LP solver described in cuPDLPx: A Further Enhanced GPU-Based First-Order Solver for Linear Programming.

For a detailed explanation of the methodology, please refer to our paper: D-PDLP: Scaling PDLP to Distributed Multi-GPU Systems.

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Problem Formulation

Consistent with cuPDLPx, D-PDLP solves linear programs in the standard form:

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

Installation

To use the solver, you must compile the project using CMake.

Requirements

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

Build from Source

Clone the repository and compile the project using CMake.

git clone git@github.com:Lhongpei/D-PDLP.git
cd D-PDLP
cmake -B build
cmake --build build --clean-first

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

Usage

The executable supports both single-GPU and multi-GPU distributed modes. It automatically detects the mode based on the MPI launcher.

1. Single GPU Mode

Run the solver directly without MPI to use a single GPU.

./build/cupdlpx-dist <MPS_FILE> <OUTPUT_DIR> [OPTIONS]

2. Distributed Multi-GPU Mode

Use mpirun to launch the solver across multiple GPUs.

mpirun -n <NUM_GPU> ./build/cupdlpx-dist <MPS_FILE> <OUTPUT_DIR> [OPTIONS]

Command Line Arguments

Positional Arguments:

1. <MPS_FILE>: Path to the input LP (supports .mps and .mps.gz).
2. <OUTPUT_DIR>: Directory where solution files will be saved.

Distributed Options:

Option	Type	Description	Default
--grid_size <r>,<c>	string	2D Grid topology (Rows x Cols)	Auto-detect
--partition_method	string	Partitioning strategy: uniform or nnz.	nnz
--permute_method	string	Matrix permutation: none, random, or block.	none

Solver Parameters:

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
--eps_opt	double	Relative optimality tolerance.	1e-4
--eps_feas	double	Relative feasibility tolerance.	1e-4
--eps_infeas_detect	double	Infeasibility detection tolerance.	1e-10
--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

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Output Artifacts

Upon successful completion, the solver generates three files in the specified output directory:

1. <PROBLEM>_summary.txt: Scalar metrics (Time, Iterations, Primal/Dual values, Residuals).
2. <PROBLEM>_primal_solution.txt: The full primal solution vector (one float per line).
3. <PROBLEM>_dual_solution.txt: The full dual solution vector (one float per line).

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Citation

If you use this software or method in your research, please cite our paper:

@misc{li2026dpdlpscalingpdlpdistributed,
      title={D-PDLP: Scaling PDLP to Distributed Multi-GPU Systems}, 
      author={Hongpei Li and Yicheng Huang and Huikang Liu and Dongdong Ge and Yinyu Ye},
      year={2026},
      eprint={2601.07628},
      archivePrefix={arXiv},
      primaryClass={math.OC},
      url={https://arxiv.org/abs/2601.07628}, 
}

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License

Copyright 2025-2026 Hongpei Li, Haihao Lu.

Licensed under the Apache License, Version 2.0. See the LICENSE file for details.