Parallel Structure-Exploiting Multistage Optimization in PIQP

Fenglong Song, Roland Schwan, Yuwen Chen, Colin Jones

Keywords: Parallel Computing, Numerical Optimization, Optimal Control, Model Predictive Control

Abstract: This paper presents a 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. 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.

Submission Number: 31