Daniel Arnström

Daniel Arnström, Emilio Benenati, Giuseppe Belgioioso

We present \texttt{DR-DAQP}, an open-source solver for strongly monotone affine variational inequaliries that combines Douglas-Rachford operator splitting with an active-set acceleration strategy. The key idea is to estimate the active set along the iterations to attempt a Newton-type correction. This step yields the exact AVI solution when the active set is correctly estimated, thus overcoming the asymptotic convergence limitation inherent in first-order methods. Moreover, we exploit warm-starting and pre-factorization of relevant matrices to further accelerate evaluation of the algorithm iterations. We prove convergence and establish conditions under which the algorithm terminates in finite time with the exact solution. Numerical experiments on randomly generated AVIs show that \texttt{DR-DAQP} is up to two orders of magnitude faster than the state-of-the-art solver \texttt{PATH}. On a game-theoretic MPC benchmark, \texttt{DR-DAQP} achieves solve times several orders of magnitude below those of the mixed-integer solver \texttt{NashOpt}. A high-performing C implementation is available at \textt{https://github.com/darnstrom/daqp}, with easily-accessible interfaces to Julia, MATLAB, and Python.

Ella J. Schmidtobreick, Daniel Arnström, Paul Häusner et al.

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.