  Gilbert proposed an algorithm for bounding the distance between a given point
and a convex set. In this article we apply the Gilbert's algorithm to get an
upper bound on the Hilbert-Schmidt distance between a given state and the set
of separable states. While Hilbert Schmidt Distance does not form a proper
entanglement measure, it can nevertheless be useful for witnessing
entanglement. We provide here a few methods based on the Gilbert's algorithm
that can reliably qualify a given state as strongly entangled or practically
separable, while being computationally efficient. The method also outputs
successively improved approximations to the Closest Separable State for the
given state. We demonstrate the efficacy of the method with examples.
