  For a class of generalized Hubbard models, we determine the maximal stability
region for the superconducting eta-pairing ground state. We exploit the
Optimized Ground State (OGS) approach and the Lanczos diagonalization procedure
to derive a sequence of improved bounds. We show that some pieces of the
stability boundary are asymptotic, namely independent on the OGS cluster size.
In this way, necessary and sufficient conditions are obtained to realize
superconductivity in terms of an eta-pairing ground state. The phenomenon is
explained by studying the properties of certain exact eigenstates of the OGS
hamiltonians.
