D-PDLP

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A First-Order LP Solver Accelerated on Multiple GPUs

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

[![License](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](https://raw.githubusercontent.com/Lhongpei/D-PDLP/main/LICENSE)
[![arXiv](https://img.shields.io/badge/arXiv-2601.07628-B31B1B.svg)](https://arxiv.org/pdf/2601.07628)

**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](https://github.com/Lhongpei/cuPDLPx), a GPU-accelerated LP solver described in [cuPDLPx: A Further Enhanced GPU-Based First-Order Solver for Linear Programming](https://arxiv.org/abs/2507.14051).

For a detailed explanation of the methodology, please refer to our paper: [D-PDLP: Scaling PDLP to Distributed Multi-GPU Systems](https://arxiv.org/pdf/2601.07628).

---

## Problem Formulation

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

```math
\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 Tools:** MPI, NCCL.
* **Others:** OpenMP.
### Build from Source
Clone the repository and compile the project using CMake.
```bash
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.

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

```

### 2. Distributed Multi-GPU Mode

Use `mpirun` to launch the solver across multiple GPUs.

```bash
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. Missing parent directories are created automatically.

**Distributed Options:**

---

## 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).

---

## Citation

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

```bibtex
@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},
}
```

---

## License

Licensed under the Apache License, Version 2.0. See the [LICENSE](LICENSE) file for details.

D-PDLP

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