# ReLU-QP: A GPU-Accelerated Quadratic Programming Solver for Model-Predictive Control

arXiv: https://arxiv.org/abs/2311.18056 · HTML: https://mlsanity.com/paper/2311.18056/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2023.

## Built on by (most cited first, 7 of 7)

- [Dexonomy: Synthesizing All Dexterous Grasp Types in a Grasp Taxonomy](https://mlsanity.com/paper/2504.18829/) (2025)
- [Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2510.06179/) (2025)
- [Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://mlsanity.com/paper/2604.07644/) (2026)
- [Accelerating and Scaling MPC-Guided Reinforcement Learning for Humanoid Locomotion and Manipulation](https://mlsanity.com/paper/2606.05687/) (2026)
- [TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2606.24039/) (2026)
- [FORGE: Verification-Gated Behavioral Repair for Generative Language Models](https://mlsanity.com/paper/2610.05190/) (2026)
- [ASM-6D: Fast Certified Pose-Shape Inference with Complete Correspondence Flow Maps](https://mlsanity.com/paper/2610.15287/) (2026)

## Abstract (arXiv)

We present ReLU-QP, a GPU-accelerated solver for quadratic programs (QPs) that is capable of solving high-dimensional control problems at real-time rates. ReLU-QP is derived by exactly reformulating the Alternating Direction Method of Multipliers (ADMM) algorithm for solving QPs as a deep, weight-tied neural network with rectified linear unit (ReLU) activations. This reformulation enables the deployment of ReLU-QP on GPUs using standard machine-learning toolboxes. We evaluate the performance of ReLU-QP across three model-predictive control (MPC) benchmarks: stabilizing random linear dynamical systems with control limits, balancing an Atlas humanoid robot on a single foot, and tracking whole-body reference trajectories on a quadruped equipped with a six-degree-of-freedom arm. These benchmarks indicate that ReLU-QP is competitive with state-of-the-art CPU-based solvers for small-to-medium-scale problems and offers order-of-magnitude speed improvements for larger-scale problems.