Authors Kohei Hayashi, Yuichi Yoshida Abstract 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 $n$: $z^*=\min_{\bv \in \bbR^n}\bracket{\bv}{A \bv} + n\bracket{\bv}{\diag(\bd)\bv} + n\bracket{\bb}{\bv}$, where $A \in \bbR^{n \times n}$ is a