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arXiv · 2511.13174

Warm-starting active-set solvers using graph neural networks

Ella J. Schmidtobreick·Daniel Arnström·Paul Häusner·Jens Sjölund
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Abstract

Quadratic programming (QP) solvers are widely used in real-time control and optimization, but their computational cost often limits applicability in time-critical settings. To resolve this, we propose a learning-to-optimize approach using graph neural networks (GNNs) to predict active constraints in the dual active-set solver DAQP. Our method exploits the structural properties of QPs by representing them as bipartite graphs and learns to approximate the optimal active set for effectively warm-starting the solver. Across varying problem sizes, the GNN consistently reduces the number of solver iterations compared to cold-starting, while performance is comparable to a multilayer perceptron baseline. In contrast to the baseline, our GNN-based approach trained on varying problem sizes generalizes to unseen dimensions, demonstrating flexibility and scalability. These results highlight the potential of structure-aware learning to accelerate optimization in real-time applications such as model predictive control.

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Ella J. Schmidtobreick, Daniel Arnström, Paul Häusner, Jens Sjölund. 2025-11-17. Warm-starting active-set solvers using graph neural networks. https://arxiv.org/abs/2511.13174

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