{"ID":2847034,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.00946","arxiv_id":"2511.00946","title":"Parallel KKT Solver in PIQP for Multistage Optimization","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.","short_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 K...","url_abs":"https://arxiv.org/abs/2511.00946","url_pdf":"https://arxiv.org/pdf/2511.00946v1","authors":"[\"Fenglong Song\",\"Roland Schwan\",\"Yuwen Chen\",\"Colin N. Jones\"]","published":"2025-11-02T14:10:37Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}