On optimization of systems governed by implicit complementarity problems*

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Abstract
We consider a class of parameter-dependent implicit complementarity problems possessing for each value of the parameter (control) from a given set a unique solution. Then an optimization problem can be formulated in which such an implicit complementarity problem arises as a constraint. We analyze 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.