  A numerical approach is presented that allows to compute nonequilibrium
steady state properties of strongly correlated quantum many-body systems. The
method is imbedded in the Keldysh Green's function formalism and is based upon
the idea of the variational cluster approach as far as the treatment of strong
correlations is concerned. It appears that the variational aspect is crucial as
it allows for a suitable optimization of a "reference" system to the
nonequilibrium target state. The approach is neither perturbative in the
many-body interaction nor in the field, that drives the system out of
equilibrium, and it allows to study strong perturbations and nonlinear
responses of systems in which also the correlated region is spatially extended.
We apply the presented approach to non-linear transport across a strongly
correlated quantum wire described by the fermionic Hubbard model. We illustrate
how the method bridges to cluster dynamical mean-field theory upon coupling two
baths containing and increasing number of uncorrelated sites.
