SCIENCE@home

Minimizing Quadratic Functions in Constant Time

K. Hayashi,Yuichi Yoshida

Published 2016 in Neural Information Processing Systems

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 $n$: $z^*=\min_{\mathbf{v} \in \mathbb{R}^n}\langle\mathbf{v}, A \mathbf{v}\rangle + n\langle\mathbf{v}, \mathrm{diag}(\mathbf{d})\mathbf{v}\rangle + n\langle\mathbf{b}, \mathbf{v}\rangle$, 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 approximated solution $z$ satisfies $|z - z^*| = O(\epsilon n^2)$ with probability $1-\delta$. The empirical performance (accuracy and runtime) is positively confirmed by numerical experiments.

PUBLICATION RECORD

  • Publication year

    2016

  • Venue

    Neural Information Processing Systems

  • Publication date

    2016-08-01

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 1608.07179
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

CITATION MAP

EXTRACTION MAP

CLAIMS

  • No claims are published for this paper.

CONCEPTS

  • No concepts are published for this paper.

REFERENCES

Showing 1-25 of 25 references · Page 1 of 1

CITED BY

Showing 1-7 of 7 citing papers · Page 1 of 1