  We present a numerical method for solving the separability problem of
Gaussian quantum states in continuous-variable quantum systems. We show that
the separability problem can be cast as an equivalent problem of determining
the feasibility of a set of linear matrix inequalities. Thus, it can be
efficiently solved using existent numerical solvers. We apply this method to
the identification of bound entangled Gaussian states. We show that the
proposed method can be used to identify bound entangled Gaussian states that
could be simple enough to be producible in quantum optics.
