  We address the problem of quantum nonlocality with positive operator valued
measures (POVM) in the context of Einstein-Podolsky-Rosen quantum steering. We
show that, given a candidate for local hidden state (LHS) ensemble, the problem
of determining the steerability of a bipartite quantum state of finite
dimension with POVMs can be formulated as a nesting problem of two convex
objects. One consequence of this is the strengthening of the theorem that
justifies choosing the LHS ensemble based on symmetry of the bipartite state.
As a more practical application, we study the classic problem of the
steerability of two-qubit Werner states with POVMs. We show strong numerical
evidence that these states are unsteerable with POVMs up to a mixing
probability of $\frac{1}{2}$ within an accuracy of $10^{-3}$.
