NeuralQP: A General Hypergraph-based Optimization Framework for Large-scale Quadratically Constrained Quadratic Programs
Primary Area: optimization
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Keywords: Quadratically Constrained Quadratic Programs, Machine Learning, Optimization
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TL;DR: NeuralQP is a general hypergraph-based optimization framework for large-scale QCQPs.
Abstract: Machine Learning (ML)-based optimization frameworks have drawn increasing attention for their remarkable ability to accelerate the optimization procedure of large-scale Quadratically Constrained Quadratic Programs (QCQPs) by learning the shared problem structures, resulting in improved performance compared to classical solvers. However, current ML-based frameworks often struggle with strong problem assumptions and high dependence on large-scale solvers. This paper presents a promising and general hypergraph-based optimization framework for large-scale QCQPs, called NeuralQP. The proposed method comprises two key components: Hypergraph-based Neural Prediction, which generates the embedding of an arbitrary QCQP and obtains the predicted solution without any problem assumption; Iterative Neighborhood Optimization, which uses a McCormick relaxation-based repair strategy to quickly identify illegal variables in the predicted solution and iteratively improves the current solution using only a small-scale solver. Experiments on three classic benchmarks demonstrate that NeuralQP converges significantly faster than the state-of-the-art solves (e.g. Gurobi), further validating the efficiency of the ML-based framework for QCQPs.
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Submission Number: 2687
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