# A Complete Semidefinite Algorithm for Detecting Copositive Matrices and Tensors

arXiv: https://arxiv.org/abs/1711.03704 · HTML: https://mlsanity.com/paper/1711.03704/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2017.

## Built on by (most cited first, 1 of 1)

- [Higher Order Correlation Analysis for Multi-View Learning](https://mlsanity.com/paper/2201.11949/) (2022)

## Abstract (arXiv)

A real symmetric matrix (resp., tensor) is said to be copositive if the associated quadratic (resp., homogeneous) form is greater than or equal to zero over the nonnegative orthant. The problem of detecting their copositivity is NP-hard. This paper proposes a complete semidefinite relaxation algorithm for detecting the copositivity of a matrix or tensor. If it is copositive, the algorithm can get a certificate for the copositivity. If it is not, the algorithm can get a point that refutes the copositivity. We show that the detection can be done by solving a finite number of semidefinite relaxations, for all matrices and tensors.