Summary: We consider a class of parameter-dependent implicit complementarity problems possessing a unique solution for each value of the parameter (control) from a given set. Then an optimization problem can be formulated in which such an implicit complementarity problem arises as a constraint. We analyse these optimization problems with the tools of nonsmooth analysis and propose an approach to their numerical solution, using a bundle method from nondifferentiable optimization and a nonsmooth variant of the Newton method. As a test example, the so-called packaging problem known from the optimum shape design is taken, in which, however, the standard rigid obstacle is replaced by an elastic one.