{"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/eiqp-execution-time-certified-and","title":"EIQP: Execution-time-certified and Infeasibility-detecting QP Solver","arxiv_id":"2502.07738","date":"2025-02-11","proceeding":null,"authors":["Liang Wu","Wei Xiao","Richard D. Braatz"],"abstract":"Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can either return a solution within a predefined level of optimality or detect QP infeasibility before the predefined sampling time is a pressing requirement. This article considers convex QP (including linear programming) and adopts its homogeneous formulation to achieve infeasibility detection. Exploiting this homogeneous formulation, this article proposes a novel infeasible interior-point method (IPM) algorithm with the best theoretical $O(\\sqrt{n})$ iteration complexity that feasible IPM algorithms enjoy. The iteration complexity is proved to be \\textit{exact} (rather than an upper bound), \\textit{simple to calculate}, and \\textit{data independent}, with the value $\\left\\lceil\\frac{\\log(\\frac{n+1}{\\epsilon})}{-\\log(1-\\frac{0.414213}{\\sqrt{n+1}})}\\right\\rceil$ (where $n$ and $\\epsilon$ denote the number of constraints and the predefined optimality level, respectively), making it appealing to certify the execution time of online time-varying convex QPs. The proposed algorithm is simple to implement without requiring a line search procedure (uses the full Newton step), and its C-code implementation (offering MATLAB, Julia, and Python interfaces) and numerical examples are publicly available at https://github.com/liangwu2019/EIQP.","url_abs":"https://arxiv.org/abs/2502.07738v2","url_pdf":"https://arxiv.org/pdf/2502.07738v2.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":"eiqp-execution-time-certified-and","repo_url":"https://github.com/liangwu2019/eiqp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"c-code","task_name":"C++ code"},{"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}