# GPU Acceleration of ADMM for Large-Scale Quadratic Programming

arXiv: https://arxiv.org/abs/1912.04263 · HTML: https://mlsanity.com/paper/1912.04263/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2019.

## Built on by (most cited first, 16 of 16)

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- [TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2606.24039/) (2026)
- [Learning the Efficient Frontier](https://mlsanity.com/paper/2309.15775/) (2023)
- [Batched First-Order Methods for Parallel LP Solving in MIP](https://mlsanity.com/paper/2601.21990/) (2026)
- [ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI](https://mlsanity.com/paper/2602.16005/) (2026)
- [Accelerated Dynamic Importance Weighting with Versatile Divergence-Minimizing Estimators](https://mlsanity.com/paper/2605.25499/) (2026)

## Abstract (arXiv)

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.