  In this article a special class of nonlinear optimal control problems
involving a bilinear term in the boundary condition is studied. These kind of
problems arise for instance in the identification of an unknown space-dependent
Robin coefficient from a given measurement of the state, or when the Robin
coefficient can be controlled in order to reach a desired state. To this end,
necessary and sufficient optimality conditions are derived and several
discretization approaches for the numerical solution the optimal control
problem are investigated. Considered are both a full discretization and the
postprocessing approach meaning that we compute an improved control by a
pointwise evaluation of the first-order optimality condition. For both
approaches finite element error estimates are shown and the validity of these
results is confirmed by numerical experiments.
