  We determine the BPS bounds in minimal gauged supergravity in four spacetime
dimensions. We concentrate on asymptotically anti-de Sitter (AdS) spacetimes,
and find that there exist two disconnected BPS ground states of the theory,
depending on the presence of magnetic charge. Each of these ground states comes
with a different superalgebra and a different BPS bound, which we derive. As a
byproduct, we also demonstrate how the supersymmetry algebra has a built-in
holographic renormalization method to define finite conserved charges.
