cuPDLP-C: A Strengthened Implementation of cuPDLP for Linear Programming by C language

TL;DR

This paper presents a re-implementation of cuPDLP in C language, significantly enhancing its computational efficiency on large-scale linear programming problems and demonstrating advantages over commercial solvers.

Contribution

Re-implemented and optimized cuPDLP in C language, achieving improved performance and computational advantages on large-scale linear programming problems.

Findings

cuPDLP in C outperforms commercial solvers on large-scale problems

GPU-based cuPDLP achieves near-commercial solver performance

Optimization in C enhances efficiency over previous Julia implementation

Abstract

A recent GPU implementation of the Restarted Primal-Dual Hybrid Gradient Method for Linear Programming was proposed in Lu and Yang (2023). Its computational results demonstrate the significant computational advantages of the GPU-based first-order algorithm on certain large-scale problems. The average performance also achieves a level close to commercial solvers for the first time in history. However, due to limitations in experimental hardware and the disadvantage of implementing the algorithm in Julia compared to C language, neither the commercial solver nor cuPDLP reached their maximum efficiency. Therefore, in this report, we have re-implemented and optimized cuPDLP in C language. Utilizing state-of-the-art CPU and GPU hardware, we extensively compare cuPDLP with the best commercial solvers. The experiments further highlight its substantial computational advantages and potential for solving large-scale linear programming problems. We also discuss the profound impact this breakthrough may have on mathematical programming research and the entire operations research community.