GPU Acceleration of ADMM for Large-Scale Quadratic Programming

TL;DR

This paper demonstrates how leveraging GPU parallel computing significantly accelerates ADMM for large-scale quadratic programming, achieving up to 100x speedup over CPU implementations.

Contribution

It introduces a GPU-accelerated ADMM solver built on OSQP, showcasing substantial performance improvements for large-scale problems.

Findings

GPU implementation is up to 100 times faster than CPU

Parallelization effectively exploits GPU architecture

Open-source CUDA implementation validated on large problems

Abstract

The alternating direction method of multipliers (ADMM) is a powerful operator splitting technique for solving structured convex optimization problems. Due to its relatively low per-iteration computational cost and ability to exploit sparsity in the problem data, it is particularly suitable for large-scale optimization. However, the method may still take prohibitively long to compute solutions to very large problem instances. Although ADMM is known to be parallelizable, this feature is rarely exploited in real implementations. In this paper we exploit the parallel computing architecture of a graphics processing unit (GPU) to accelerate ADMM. We build our solver on top of OSQP, a state-of-the-art implementation of ADMM for quadratic programming. Our open-source CUDA C implementation has been tested on many large-scale problems and was shown to be up to two orders of magnitude faster than the CPU implementation.