{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/an-execution-time-certified-qp-algorithm-for","title":"A Parallel Vector-form $LDL^\\top$ Decomposition for Accelerating Execution-time-certified $\\ell_1$-penalty Soft-constrained MPC","arxiv_id":"2403.18235","date":"2024-03-27","proceeding":null,"authors":["Liang Wu","Liwei Zhou","Richard D. Braatz"],"abstract":"Handling possible infeasibility and providing an execution time certificate are two pressing requirements of real-time Model Predictive Control (MPC). To meet these two requirements simultaneously, this paper proposes an $\\ell_1$-penalty soft-constrained MPC formulation that is globally feasible and solvable with an execution time certificate using our proposed algorithm. This paper proves for the first time that $\\ell_1$-penalty soft-constrained MPC problems can be equivalently transformed into a box-constrained quadratic programming (Box-QP) and then our previous execution-time-certified algorithm \\cite{wu2023direct} (only limited to Box-QP) can be applied. However, our previous Box-QP algorithm \\cite{wu2023direct}, which provides a theoretical execution-time certificate, is conservative in its iteration analysis, thus sacrificing computation efficiency. To this end, this paper proposes a novel $LDL^\\top$ decomposition for the first time, to accelerate the computation of Newton step at each iteration. The speedup of our $LDL^\\top$ decomposition comes from two-fold: \\textit{i)} exploitation of the fact that the number of inequality constraints is generally larger than the number of variables in condensed MPC formulations, \\textit{ii)} vectorized and parallel implementation based on based on its vector-wise operations, instead of element-wise operations of previous decomposition methods. Numerical experiments demonstrate great speedups of the proposed $LDL^\\top$ decomposition (even up to 1000-fold, compared to the standard Choleksky method), which thus helps our solver achieve comparable computation performance to the state-of-the-art solvers such as IPOPT and OSQP. Code is available at \\url{https://github.com/liangwu2019/L1-penalty-QP}.","url_abs":"https://arxiv.org/abs/2403.18235v3","url_pdf":"https://arxiv.org/pdf/2403.18235v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"an-execution-time-certified-qp-algorithm-for","repo_url":"https://github.com/liangwu2019/l1-penalty-qp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"form","task_name":"Form"},{"task_slug":"model-predictive-control","task_name":"Model Predictive Control"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}