We present SCQPTH: a differentiable first-order splitting method for convex quadratic programs. The SCQPTH framework is based on the alternating direction method of multipliers (ADMM) and the software implementation is motivated by the state-of-the art solver OSQP: an operating splitting solver for convex quadratic programs (QPs). The SCQPTH software is made available as an open-source python package and contains many similar features including efficient reuse of matrix factorizations, infeasibility detection, automatic scaling and parameter selection. The forward pass algorithm performs operator splitting in the dimension of the original problem space and is therefore suitable for large scale QPs with $100-1000$ decision variables and thousands of constraints. Backpropagation is performed by implicit differentiation of the ADMM fixed-point mapping. Experiments demonstrate that for large scale QPs, SCQPTH can provide a $1\times - 10\times$ improvement in computational efficiency in comparison to existing differentiable QP solvers.

翻译：我们提出SCQPTH：一种用于凸二次规划的可微一阶分裂方法。SCQPTH框架基于交替方向乘子法（ADMM），其软件实现受先进求解器OSQP（一种用于凸二次规划（QP）的算子分裂求解器）的启发。SCQPTH软件以开源Python包的形式提供，包含诸多类似特性，包括矩阵分解的高效重用、不可行性检测、自动缩放和参数选择。前向传播算法在原始问题空间的维度上执行算子分裂，因此适用于具有$100-1000$个决策变量和数千个约束的大规模QP。反向传播通过ADMM不动点映射的隐式微分实现。实验表明，对于大规模QP，与现有可微QP求解器相比，SCQPTH的计算效率可提升$1\times - 10\times$。