An algorithm for determining copositive matrices

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 ${\widehat{T}}^{-}=\{y\in {\mathrm{\Delta }}_m\mathrm{\mid }{\beta }^{T}y\le 0\}$ on the standard simplex ${\mathrm{\Delta }}_m$, where each component of the vector $\beta$ is -1, 0 or 1.