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.

翻译：我们提出`DR-DAQP`，一种面向强单调仿射变分不等式的开源求解器，它结合了Douglas-Rachford算子分裂方法与积极集加速策略。其核心思想是在迭代过程中估计积极集，以尝试牛顿型校正。当积极集被正确估计时，该步骤可精确求解仿射变分不等式，从而克服一阶方法固有的渐近收敛局限性。此外，我们利用热启动和关键矩阵的预分解进一步加速算法迭代的求值过程。我们证明了该算法的收敛性，并给出了算法在有限步内终止于精确解的条件。基于随机生成的仿射变分不等式的数值实验表明，`DR-DAQP`的速度比当前最先进的求解器`PATH`快两个数量级。在博弈论模型预测控制基准测试中，`DR-DAQP`的求解时间比混合整数求解器`NashOpt`低数个数量级。高性能C语言实现代码见`https://github.com/darnstrom/daqp`，并提供Julia、MATLAB和Python的便捷接口。