  The present paper represents a continuation of our previous one. There, a
continuous dependence result for the solution of an elliptic
variational-hemivariational inequality was obtained and then used to prove the
existence of optimal pairs for two associated optimal control problems. In the
current paper we complete this study with more general results. Indeed, we
prove the continuous dependence of the solution with respect to a parameter
which appears in all the data of the problem, including the set of constraints,
the nonlinear operator and the two functionals which govern the
variational-hemivariational inequality. This allows us to consider a general
associated optimal control problem for which we prove the existence of optimal
pairs, together with a new convergence result. The mathematical tools developed
in this paper are useful in the analysis and control of a large class of
boundary value problems which, in a weak formulation, lead to elliptic
variational-hemivariational inequalities. To provide an example, we illustrate
our results in the study of an inequality which describes the equilibrium of an
elastic body in frictional contact with a foundation made of a rigid body
covered by a layer of soft material.
