  We introduce a nested optimization procedure using semi-definite relaxation
for the fitting step in Hamiltonian-based cluster dynamical mean-field theory
(DMFT) methodologies. We show that the proposed method is more efficient and
flexible than state-of-the-art fitting schemes, which allows us to treat as
large a number of bath sites as the impurity solver at hand allows. We
characterize its robustness to initial conditions and symmetry constraints,
thus providing conclusive evidence that in the presence of a large bath, our
semi-definite relaxation approach can find the correct set of bath parameters
without needing to include \emph{a priori} knowledge of the properties that are
to be described. We believe this method will be of great use for
Hamiltonian-based calculations, simplifying and improving one of the key steps
in cluster dynamical mean-field theory calculations.

Strongly Correlated Electrons;Computational Physics