Warm-starting active-set solvers using graph neural networks

• URL: http://arxiv.org/abs/2511.13174v1
• Date: Mon, 17 Nov 2025 09:22:45 GMT
• Title: Warm-starting active-set solvers using graph neural networks
• Authors: Ella J. Schmidtobreick, Daniel Arnström, Paul Häusner, Jens Sjölund,
• Abstract summary: We propose a learning-to-optimize approach using graph neural networks (GNNs) to predict active sets in the dual active-set solver DAQP.<n>Across varying problem sizes, the GNN consistently reduces the number of solver iterations compared to cold-starting.<n>A GNN trained on varying problem sizes generalizes effectively to unseen dimensions, demonstrating flexibility and scalability.
• Score: 4.309217525488745
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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. We propose a learning-to-optimize approach using graph neural networks (GNNs) to predict active sets in the dual active-set solver DAQP. The method exploits the structural properties of QPs by representing them as bipartite graphs and learning to identify the optimal active set for efficiently 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 (MLP) baseline. Furthermore, a GNN trained on varying problem sizes generalizes effectively 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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