SCQPTH：一种用于凸二次规划的高效可微分裂方法
SCQPTH: an efficient differentiable splitting method for convex quadratic programming
AI总结：
本文提出基于 ADMM 的可微凸二次规划求解器 SCQPTH，支持大规模问题并通过隐式微分反向传播，实验显示其效率较现有求解器提升 1×–10×。
摘要：
我们提出了 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），其软件实现受到最先进求解器 OSQP 的启发：OSQP 是一种用于凸二次规划（QP）的算子分裂求解器。SCQPTH 软件作为开源 Python 包提供，并包含许多类似功能，包括矩阵分解的高效复用、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中执行算子分裂，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。反向传播通过对 ADMM 不动点映射进行隐式微分来执行。实验表明，对于大规模 QP，与现有可微 QP 求解器相比，SCQPTH 可提供 1×–10× 的计算效率提升。
英文摘要：
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.
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