NeuralQP: A General Hypergraph-based Optimization Framework for Large-scale QCQPs
<|reference_start|>NeuralQP: A General Hypergraph-based Optimization Framework for Large-scale QCQPs: 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.<|reference_end|>
@article{xiong2024neuralqp:,
    title={NeuralQP: A General Hypergraph-based Optimization Framework for
  Large-scale QCQPs},
    author={Zhixiao Xiong, Fangyu Zong, Huigen Ye, Hua Xu},
    journal={arXiv preprint arXiv:2410.03720},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.03720},
    primaryClass={math.OC cs.LG}
}