Testing copositivity with the help of difference-of-convex optimization

We consider the problem of minimizing an indefinite quadratic function over the nonnegative orthant, or equivalently, the problem of deciding whether a symmetric matrix is copositive. We formulate the problem as a difference of convex functions (d.c.) problem. Using conjugate duality, we show that there is a one-to-one correspondence between their respective stationary points and minima. We then apply a subgradient algorithm to approximate those stationary points and obtain an efficient heuristic to verify non-copositivity of a matrix.