  We address the reliability of the Optimized Perturbation Theory (OPT) in the
context of the 0-dimensional $O(N)$ scalar field model. The effective
potential, the self-energy and the 1PI four-point Green's function for the
model are computed using different optimization schemes and the results
contrasted to the exact results for the model. Our results are also compared to
those obtained with the $1/N$-expansion and with those from ordinary
perturbation theory. The OPT results are shown to be stable even at large
couplings and to have better convergence properties than the ones produced in
the $1/N$-expansion. It is also shown that the principle of minimal sensitive
optimization procedure used in conjunction with the OPT method tends to always
produce better results, in particular when applied directly to the self-energy.
