  We consider gradient descent and quasi-Newton algorithms to optimize the full
configuration interaction (FCI) ground state wavefunction starting from an
arbitrary reference state $|0 \rangle$. We show that the energies obtained
along the optimization path can be evaluated in terms of expectation values of
$|0 \rangle$, thus avoiding explicit storage of intermediate wavefunctions.
This allows us to find the energies after the first few steps of the FCI
algorithm for systems much larger than what standard, deterministic FCI codes
can handle at present. We show an application of the algorithm with reference
wavefunctions constructed as linear combinations of non-orthogonal
determinants.
