SCQPTH: an efficient differentiable splitting method for convex
  quadratic programming
Andrew Butler
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.