Accelerating a Linear Programming Algorithm on AMD GPUs

TL;DR

This paper presents a GPU-accelerated implementation of a linear programming algorithm on AMD hardware, achieving up to 36x speedup over CPU solutions for large-scale problems, thus enhancing efficiency in industrial applications.

Contribution

It introduces a high-performance, open-source GPU implementation of the PDHG algorithm tailored for AMD GPUs, addressing scalability and latency issues in LP solving.

Findings

Up to 36x speedup on AMD GPUs compared to CPU solvers.

Effective handling of large-scale, real-world LP problems.

Demonstrated advantages of GPU acceleration in industrial optimization.

Abstract

Linear Programming (LP) is a foundational optimization technique with widespread applications in finance, energy trading, and supply chain logistics. However, traditional Central Processing Unit (CPU)-based LP solvers often struggle to meet the latency and scalability demands of dynamic, high-dimensional industrial environments, creating a significant computational challenge. This project addresses these limitations by accelerating linear programming on AMD Graphics Processing Units (GPUs), leveraging the ROCm open-source platform and PyTorch. The core of this work is the development of a robust, high-performance, open-source implementation of the Primal-Dual Hybrid Gradient (PDHG) algorithm, engineered specifically for general LP problems on AMD hardware. Performance is evaluated against standard LP test sets and established CPU-based solvers, with a particular focus on challenging real- world instances including the Security-Constrained Economic Dispatch (SCED) to guide hyperparameter tuning. Our results show a significant improvement, with up to a 36x speedup on GPU over CPU for large-scale problems, highlighting the advantages of GPU acceleration in solving complex optimization tasks.