# Parallel KKT Solver in PIQP for Multistage Optimization

arXiv: https://arxiv.org/abs/2511.00946 · HTML: https://mlsanity.com/paper/2511.00946/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2025.

## Built on by (most cited first, 1 of 1)

- [TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2606.24039/) (2026)

## Abstract (arXiv)

This paper presents an efficient parallel Cholesky factorization and triangular solve algorithm for the Karush-Kuhn-Tucker (KKT) systems arising in multistage optimization problems, with a focus on model predictive control and trajectory optimization for racing. The proposed approach directly parallelizes solving the KKT systems with block-tridiagonal-arrow KKT matrices on the linear algebra level arising in interior-point methods. The algorithm is implemented as a new backend of the PIQP solver and released as open source. Numerical experiments on the chain-of-masses benchmarks and a minimum curvature race line optimization problem demonstrate substantial performance gains compared to other state-of-the-art solvers.