For a class of quasi-variational inequalities (QVIs) of obstacle-type the
stability of its solution set and associated optimal control problems are
considered. These optimal control problems are non-standard in the sense that
they involve an objective with set-valued arguments. The approach to study the
solution stability is based on perturbations of minimal and maximal elements of
the solution set of the QVI with respect to {monotone} perturbations of the
forcing term. It is shown that different assumptions are required for studying
decreasing and increasing perturbations and that the optimization problem of
interest is well-posed.Comment: 29 page