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‎LICENSE‎

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Apache License
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‎Makefile‎

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# Compiler
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CC = gcc
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NVCC = nvcc
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LINKER = nvcc
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SYSTEM_GXX := $(shell which g++)
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SRC_DIR = ./cupdlpx
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BUILD_DIR = ./build
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# CFLAGS for C compiler (gcc)
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CFLAGS = -I. -I$(CUDA_HOME)/include -O3 -Wall -Wextra -g
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# NVCCFLAGS for CUDA compiler (nvcc)
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NVCCFLAGS = -I. -I$(CUDA_HOME)/include -O3 -g -gencode arch=compute_90,code=sm_90 -gencode arch=compute_80,code=sm_80 -Xcompiler -gdwarf-4 -ccbin $(SYSTEM_GXX)
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# LDFLAGS for the linker
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LDFLAGS = -L$(CONDA_PREFIX)/lib -L$(CUDA_HOME)/lib64 -lcudart -lcusparse -lcublas -lz -lm
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C_SOURCES = $(filter-out $(SRC_DIR)/cupdlpx.c, $(wildcard $(SRC_DIR)/*.c))
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CU_SOURCES = $(wildcard $(SRC_DIR)/*.cu)
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C_OBJECTS = $(patsubst $(SRC_DIR)/%.c, $(BUILD_DIR)/%.o, $(C_SOURCES))
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CU_OBJECTS = $(patsubst $(SRC_DIR)/%.cu, $(BUILD_DIR)/%.o, $(CU_SOURCES))
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OBJECTS = $(C_OBJECTS) $(CU_OBJECTS)
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TARGET_LIB = $(BUILD_DIR)/libcupdlpx.a
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DEBUG_SRC = $(SRC_DIR)/cupdlpx.c
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DEBUG_EXEC = $(BUILD_DIR)/cupdlpx
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.PHONY: all clean build
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all: $(TARGET_LIB)
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$(TARGET_LIB): $(OBJECTS)
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@echo "Archiving objects into $(TARGET_LIB)..."
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@ar rcs $@ $^
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build: $(DEBUG_EXEC)
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$(DEBUG_EXEC): $(DEBUG_SRC) $(TARGET_LIB)
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@echo "Building debug executable..."
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@$(LINKER) $(NVCCFLAGS) $(DEBUG_SRC) -o $(DEBUG_EXEC) $(TARGET_LIB) $(LDFLAGS)
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$(BUILD_DIR)/%.o: $(SRC_DIR)/%.c
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@mkdir -p $(BUILD_DIR)
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@echo "Compiling $< -> $@..."
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@$(CC) $(CFLAGS) -c $< -o $@
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$(BUILD_DIR)/%.o: $(SRC_DIR)/%.cu
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@mkdir -p $(BUILD_DIR)
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@echo "Compiling $< -> $@..."
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@$(NVCC) $(NVCCFLAGS) -c $< -o $@
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clean:
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@echo "Cleaning up..."
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@rm -rf $(BUILD_DIR) $(TARGET_LIB) $(DEBUG_EXEC)

‎README.md‎

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# **cuPDLPx: A GPU-Accelerated First-Order LP Solver**
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[![License](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](LICENSE)
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[![GitHub release](https://img.shields.io/github/release/MIT-Lu-Lab/cuPDLPx.svg)](https://github.com/MIT-Lu-Lab/cuPDLPx/releases)
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[![arXiv](https://img.shields.io/badge/arXiv-2407.16144-B31B1B.svg)](https://arxiv.org/abs/2407.16144)
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[![arXiv](https://img.shields.io/badge/arXiv-2507.14051-B31B1B.svg)](https://arxiv.org/abs/2507.14051)
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**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](https://github.com/jinwen-yang/cuPDLP.jl)**, on standard LP benchmark suites.
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Our work is presented in two papers:
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* **Computational Paper:** [cuPDLPx: A Further Enhanced GPU-Based First-Order Solver for Linear Programming](https://arxiv.org/abs/2507.14051) details the practical innovations that give **cuPDLPx** its performance edge.
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* **Theoretical Paper:** [Restarted Halpern PDHG for Linear Programming](https://arxiv.org/pdf/2407.16144) provides the mathematical foundation for our method.
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## Getting started
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Follow these steps to build the solver and verify its installation.
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### Requirements
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- An NVIDIA GPU with CUDA support (CUDA 12.x is recommended).
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- A C toolchain (gcc) and the NVIDIA CUDA Compiler (nvcc).
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### Build from Source
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Clone the repository and compile the project using `make`.
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```bash
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make clean
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make build
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```
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This will create the solver binary at `./build/cupdlpx`.
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### Verifying the Installation
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Run a small test problem to confirm that the solver was built correctly.
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```bash
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# 1. Download a test instance from the MIPLIB library
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wget -P test/ https://miplib.zib.de/WebData/instances/2club200v15p5scn.mps.gz
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# 2. Solve the problem and write output to the current directory (.)
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./build/cupdlpx test/2club200v15p5scn.mps.gz test/
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```
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If the solver runs and creates output files, your installation is successful.
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## Usage Guide
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### Command-Line Interface
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The solver is invoked with the following syntax, specifying an input file and an output directory.
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```bash
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./cupdlpx [OPTIONS] <mps_file> <output_directory>
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```
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### Arguments
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- `<mps_file>`: The path to the input linear programming problem. Both plain (`.mps`) and gzipped (`.mps.gz`) files are supported.
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- `<output_directory>`: The directory where the output files will be saved.
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### Solver Options
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| Option | Type | Description | Default |
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| :--- | :--- | :--- | :--- |
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| `-h`, `--help` | `flag` | Display the help message. | N/A |
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| `-v`, `--verbose` | `flag` | Enable verbose logging. | `false` |
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| `--time_limit` | `double` | Time limit in seconds. | `3600.0` |
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| `--iter_limit` | `int` | Iteration limit. | `2147483647` |
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| `--eps_opt` | `double` | Relative optimality tolerance. | `1e-4` |
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| `--eps_feas` | `double` | Relative feasibility tolerance. | `1e-4` |
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| `--eps_infeas_detect` | `double` | Infeasibility detection tolerance. | `1e-10` |
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### Output Files
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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:
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- `INSTANCE_summary.txt`: Contains solver statistics, timings, and termination information.
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- `INSTANCE_primal_solution.txt`: The primal solution vector.
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- `INSTANCE_dual_solution.txt`: The dual solution vector.
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## Reference
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If you use cuPDLPx or the ideas in your work, please cite the source below.
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```bibtex
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@article{lu2025cupdlpx,
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title={cuPDLPx: A Further Enhanced GPU-Based First-Order Solver for Linear Programming},
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author={Lu, Haihao and Peng, Zedong and Yang, Jinwen},
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journal={arXiv preprint arXiv:2507.14051},
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year={2025}
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}
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@article{lu2024restarted,
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title={Restarted Halpern PDHG for linear programming},
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author={Lu, Haihao and Yang, Jinwen},
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journal={arXiv preprint arXiv:2407.16144},
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year={2024}
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}
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```
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## License
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cuPDLPx is licensed under the Apache 2.0 License. See the [LICENSE](LICENSE) file for details.

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