{"paper":{"title":"Minimizing Quadratic Functions in Constant Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Kohei Hayashi, Yuichi Yoshida","submitted_at":"2016-08-25T14:43:17Z","abstract_excerpt":"A sampling-based optimization method for quadratic functions is proposed. Our method approximately solves the following $n$-dimensional quadratic minimization problem in constant time, which is independent of $n$: $z^*=\\min_{\\mathbf{v} \\in \\mathbb{R}^n}\\langle\\mathbf{v}, A \\mathbf{v}\\rangle + n\\langle\\mathbf{v}, \\mathrm{diag}(\\mathbf{d})\\mathbf{v}\\rangle + n\\langle\\mathbf{b}, \\mathbf{v}\\rangle$, where $A \\in \\mathbb{R}^{n \\times n}$ is a matrix and $\\mathbf{d},\\mathbf{b} \\in \\mathbb{R}^n$ are vectors. Our theoretical analysis specifies the number of samples $k(\\delta, \\epsilon)$ such that the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07179","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}