  We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with
operators that are monotone on a given closed convex subset. A simple stable
approach is Lavrentiev regularization, but existence of solutions of the
regularized equation on the given subset can be guaranteed only under
additional assumptions that are not satisfied in some applications.
  Lavrentiev regularization of the related variational inequality seems to be a
reasonable alternative then. For the latter approach, in this paper we present
new error estimates for suitable a priori parameter choices, if the considered
operator is cocoercive and if in addition the solution admits an adjoint source
representation. Some numerical experiments are included.
