# PIQP: A Proximal Interior-Point Quadratic Programming Solver

arXiv: https://arxiv.org/abs/2304.00290 · HTML: https://mlsanity.com/paper/2304.00290/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2023.

## Built on by (most cited first, 9 of 9)

- [Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs](https://mlsanity.com/paper/2406.05938/) (2024)
- [Differentiation Through Black-Box Quadratic Programming Solvers](https://mlsanity.com/paper/2410.06324/) (2024)
- [Enforcing convex constraints in Graph Neural Networks](https://mlsanity.com/paper/2510.11227/) (2025)
- [Efficiently Learning Robust Torque-based Locomotion Through Reinforcement with Model-Based Supervision](https://mlsanity.com/paper/2601.16109/) (2026)
- [TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2606.24039/) (2026)
- [ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI](https://mlsanity.com/paper/2602.16005/) (2026)
- [Optimizing the Induced Correlation in Omnibus Joint Graph Embeddings](https://mlsanity.com/paper/2409.17544/) (2024)
- [Reinforcement learning for adaptive interior point methods in convex quadratic programming](https://mlsanity.com/paper/2509.07404/) (2025)
- [Elastic ODYN: Differentiable Optimization for Infeasible Control and Learning in Robotics](https://mlsanity.com/paper/2606.16564/) (2026)

## Abstract (arXiv)

This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle ill-conditioned convex QP problems without the need for linear independence of the constraints. The open-source implementation is written in C++ with interfaces to C, Python, Matlab, and R leveraging the Eigen3 library. The method uses a pivoting-free factorization routine and allocation-free updates of the problem data, making the solver suitable for embedded applications. The solver is evaluated on the Maros-M'esz'aros problem set and optimal control problems, demonstrating state-of-the-art performance for both small and large-scale problems, outperforming commercial and open-source solvers.