# SCQPTH: an efficient differentiable splitting method for convex quadratic programming

arXiv: https://arxiv.org/abs/2308.08232 · HTML: https://mlsanity.com/paper/2308.08232/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 16 Aug 2023.

## Builds on (most cited first, 7 of 7)

- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Differentiating Through a Cone Program](https://mlsanity.com/paper/1904.09043/) (2019)
- [Optimal parameter selection for the alternating direction method of multipliers (ADMM): quadratic problems](https://mlsanity.com/paper/1306.2454/) (2013)
- [Efficient differentiable quadratic programming layers: an ADMM approach](https://mlsanity.com/paper/2112.07464/) (2021)
- [SuperSCS: fast and accurate large-scale conic optimization](https://mlsanity.com/paper/1903.06477/) (2019)

## Built on by (most cited first, 5 of 5)

- [Differentiation Through Black-Box Quadratic Programming Solvers](https://mlsanity.com/paper/2410.06324/) (2024)
- [A Fully First-Order Layer for Differentiable Optimization](https://mlsanity.com/paper/2512.02494/) (2025)
- [A Penalty Approach for Differentiation Through Black-Box Quadratic Programming Solvers](https://mlsanity.com/paper/2602.14154/) (2026)
- [AT-SKM-Net: An Accelerated Trainable Sampling Kaczmarz-Motzkin Framework for Linear Hard-Constraint Feasibility on Dynamic Graphs](https://mlsanity.com/paper/2609.30088/) (2026)
- [dOPT: Differentiating Conic Optimization via Geometric Reduction](https://mlsanity.com/paper/2609.33828/) (2026)

## Abstract (arXiv)

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× - 10× improvement in computational efficiency in comparison to existing differentiable QP solvers.