  This paper continues earlier work and 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. The optimization
approach in the earlier work on the inverse problem using the output-least
squares formulation involves the variational inequality of the second kind as
constraint. Here we use regularization technics of nondifferentiable
optimization, regularize the nonsmooth part in the variational inequality and
arrive at an optimization problem for which the constraint variational
inequality is replaced by the regularized variational equation. For this case,
the smoothness of the parameter-to-solution map is studied and convergence
analysis and optimality conditions are given.
