# NeuralQP: A General Hypergraph-based Optimization Framework for Large-scale QCQPs

arXiv: https://arxiv.org/abs/2410.03720 · HTML: https://mlsanity.com/paper/2410.03720/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 28 Sep 2024.

## Builds on (most cited first, 13 of 13)

- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [Online Mixed-Integer Optimization in Milliseconds](https://mlsanity.com/paper/1907.02206/) (2019)
- [Accelerating Quadratic Optimization with Reinforcement Learning](https://mlsanity.com/paper/2107.10847/) (2021)
- [The Voice of Optimization](https://mlsanity.com/paper/1812.09991/) (2018)
- [Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problems](https://mlsanity.com/paper/2310.10603/) (2023)
- [On Representing Mixed-Integer Linear Programs by Graph Neural Networks](https://mlsanity.com/paper/2210.10759/) (2022)
- [Learning for Spatial Branching: An Algorithm Selection Approach](https://mlsanity.com/paper/2204.10834/) (2022)
- [Torque Saturation in Bipedal Robotic Walking through Control Lyapunov Function Based Quadratic Programs](https://mlsanity.com/paper/1302.7314/) (2013)
- [Finding Perfect Matchings in Bipartite Hypergraphs](https://mlsanity.com/paper/1509.07007/) (2015)
- [Adaptive Constraint Partition based Optimization Framework for Large-scale Integer Linear Programming(Student Abstract)](https://mlsanity.com/paper/2211.11564/) (2022)

## Built on by (most cited first, 4 of 4)

- [Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guarantees](https://mlsanity.com/paper/2410.11061/) (2024)
- [Towards graph neural networks for provably solving convex optimization problems](https://mlsanity.com/paper/2502.02446/) (2025)
- [Towards Solving Polynomial-Objective Integer Programming with Hypergraph Neural Networks](https://mlsanity.com/paper/2603.19318/) (2026)
- [Learning to Design Convex Relaxations for Nonconvex Optimization](https://mlsanity.com/paper/2610.16948/) (2026)

## Abstract (arXiv)

Machine Learning (ML) optimization frameworks have gained attention for their ability to accelerate the optimization of large-scale Quadratically Constrained Quadratic Programs (QCQPs) by learning shared problem structures. However, existing ML frameworks often rely heavily on strong problem assumptions and large-scale solvers. This paper introduces NeuralQP, a general hypergraph-based framework for large-scale QCQPs. NeuralQP features two main components: Hypergraph-based Neural Prediction, which generates embeddings and predicted solutions for QCQPs without problem assumptions, and Parallel Neighborhood Optimization, which employs a McCormick relaxation-based repair strategy to identify and correct illegal variables, iteratively improving the solution with a small-scale solver. We further prove that our framework UniEGNN with our hypergraph representation is equivalent to the Interior-Point Method (IPM) for quadratic programming. Experiments on two benchmark problems and large-scale real-world instances from QPLIB demonstrate that NeuralQP outperforms state-of-the-art solvers (e.g., Gurobi and SCIP) in both solution quality and time efficiency, further validating the efficiency of ML optimization frameworks for QCQPs.