Warm-starting active-set solvers using graph neural networks

Ella J. Schmidtobreick, Daniel Arnström, Paul Häusner, Jens Sjölund

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.