{"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/minimizing-quadratic-functions-in-constant","title":"Minimizing Quadratic Functions in Constant Time","arxiv_id":"1608.07179","date":"2016-08-25","proceeding":"NeurIPS 2016 12","authors":["Kohei Hayashi","Yuichi Yoshida"],"abstract":"A sampling-based optimization method for quadratic functions is proposed. Our\nmethod approximately solves the following $n$-dimensional quadratic\nminimization problem in constant time, which is independent of $n$:\n$z^*=\\min_{\\mathbf{v} \\in \\mathbb{R}^n}\\langle\\mathbf{v}, A \\mathbf{v}\\rangle +\nn\\langle\\mathbf{v}, \\mathrm{diag}(\\mathbf{d})\\mathbf{v}\\rangle +\nn\\langle\\mathbf{b}, \\mathbf{v}\\rangle$, where $A \\in \\mathbb{R}^{n \\times n}$\nis a matrix and $\\mathbf{d},\\mathbf{b} \\in \\mathbb{R}^n$ are vectors. Our\ntheoretical analysis specifies the number of samples $k(\\delta, \\epsilon)$ such\nthat the approximated solution $z$ satisfies $|z - z^*| = O(\\epsilon n^2)$ with\nprobability $1-\\delta$. The empirical performance (accuracy and runtime) is\npositively confirmed by numerical experiments.","url_abs":"http://arxiv.org/abs/1608.07179v1","url_pdf":"http://arxiv.org/pdf/1608.07179v1.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":"minimizing-quadratic-functions-in-constant","repo_url":"https://github.com/hayasick/CTOQ","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}