  The local composite operator A^2 is added to the Zwanziger action, which
implements the restriction to the Gribov region in Euclidean Yang-Mills
theories in the Landau gauge. We prove the renormalizability of this action to
all orders of perturbation theory. This allows to study the dimension two gluon
condensate <A^2> by the local composite operator formalism when the restriction
is taken into account. The effective action is evaluated at one-loop order in
the MSbar scheme. We obtain explicit values for the Gribov parameter and for
the mass parameter due to <A^2>, but the expansion parameter turns out to be
rather large. Furthermore, an optimization of the perturbative expansion in
order to reduce the dependence on the renormalization scheme is performed. The
properties of the vacuum energy, with or without <A^2>, are investigated. It is
shown that in the original Gribov-Zwanziger formulation (without <A^2>), the
vacuum energy is always positive at 1-loop order, independently from the
renormalization scheme and scale. With <A^2>, we are unable to come to a
definite conclusion at the order considered. In the MSbar scheme, we still find
a positive vacuum energy, again with a relatively large expansion parameter,
but there are renormalization schemes in which the vacuum energy is negative,
albeit the dependence on the scheme itself appears to be strong. We recover the
well known consequences of the restriction, and this in the presence of <A^2>:
an infrared suppression of the gluon propagator and an enhancement of the ghost
propagator. This behaviour is in qualitative agreement with the results
obtained from the studies of the Schwinger-Dyson equations and from lattice
simulations.
