Parallel KKT Solver in PIQP for Multistage Optimization

TL;DR

This paper introduces a parallelized KKT solver for multistage optimization problems, significantly improving computational efficiency in applications like model predictive control and racing trajectory optimization.

Contribution

It develops a novel parallel Cholesky factorization algorithm for block-tridiagonal KKT matrices, integrated into the PIQP solver as an open-source backend.

Findings

Substantial performance improvements over existing solvers.

Effective parallelization of KKT system solutions.

Validated on benchmarks and real-world racing problems.

Abstract

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.