# Solving Quadratic Programs with Slack Variables via ADMM without Increasing the Problem Size

arXiv: https://arxiv.org/abs/2511.08451 · HTML: https://mlsanity.com/paper/2511.08451/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2025.

## Built on by (most cited first, 2 of 2)

- [TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2606.24039/) (2026)
- [AI-Assisted Discovery and Construction of a Counterexample to the Convergence of Three-Block ADMM with the Identity Matrix as its Third Constraint Block](https://mlsanity.com/paper/2608.14396/) (2026)

## Abstract (arXiv)

Proximal methods such as the Alternating Direction Method of Multipliers (ADMM) are effective at solving constrained quadratic programs (QPs). To tackle infeasible QPs, slack variables are often introduced to ensure feasibility, which changes the structure of the problem, increases its size, and slows down numerical resolution. In this letter, we propose a simple ADMM scheme to tackle QPs with slack variables without increasing the size of the original problem. The only modification is a slightly different projection in the z-update, while the rest of the algorithm remains standard. We prove that the method is equivalent to applying ADMM to the QP with additional slack variables, even though slack variables are not added. Numerical experiments show speedups of the approach.