An optimization approach to parameter identification in variational inequalities of second kind

This paper is concerned with the inverse problem of parameter identification in variational inequalities of the second kind that does not only treat the parameter linked to a bilinear form, but importantly also the parameter linked to a nonlinear non-smooth function. A new abstract framework covers frictional contact as well as other non-smooth problems from continuum mechanics. We investigate the dependance of the solution of the forward problem on these parameters and prove Lipschitz continuity results. We formulate an optimization approach to the parameter identification problem and provide a solvability result. Moreover we establish a convergence result for finite dimensional approximation in the optimization approach.