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This paper continues earlier work and is concerned with the inverse problemof parameter identification in variational inequalities of the second kind thatdoes not only treat the parameter linked to a bilinear form, but importantlyalso the parameter linked to a nonlinear non-smooth function. The optimizationapproach in the earlier work on the inverse problem using the output-leastsquares formulation involves the variational inequality of the second kind asconstraint. Here we use regularization technics of nondifferentiableoptimization, regularize the nonsmooth part in the variational inequality andarrive at an optimization problem for which the constraint variationalinequality is replaced by the regularized variational equation. For this case,the smoothness of the parameter-to-solution map is studied and convergenceanalysis and optimality conditions are given.

An Optimization Approach to Parameter Identification in Variational Inequalities of Second Kind -- II