DR-DAQP: A Hybrid Operator Splitting and Active-Set Solver for Affine Variational Inequalities

We present DR-DAQP, an open-source solver for strongly monotone affine variational inequalities (AVIs) 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 directly computing a point that satisfies the optimality conditions. 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 a randomly generated set of AVIs and on a set of multi-agent optimal control problems show that DR-DAQP outperforms several state-of-the-art solvers. A high-performing C implementation is available at https://github.com/darnstrom/daqp, with easily-accessible interfaces to Julia, MATLAB, and Python.