An algorithm for determining copositive matrices

TL;DR

This paper introduces COPOMATRIX, an exponential growth algorithm that determines copositivity of real symmetric matrices using a decomposition theorem and simplicial subdivision.

Contribution

The paper presents a novel exponential-time algorithm for copositivity testing based on a new decomposition theorem and simplicial subdivision techniques.

Findings

Algorithm effectively determines copositivity of symmetric matrices.

Uses decomposition theorem for simplicial subdivision.

Provides a systematic approach for copositivity testing.

Abstract

In this paper, we present an algorithm of simple exponential growth called COPOMATRIX for determining the copositivity of a real symmetric matrix. The core of this algorithm is a decomposition theorem, which is used to deal with simplicial subdivision of $\hat{T}^{-}=\{y\in \Delta_{m}| \beta^Ty\leq 0\}$ on the standard simplex $\Delta_m$, where each component of the vector $\beta$ is -1, 0 or 1.