Update strategies for perturbed nonsmooth equations

Nonsmooth operator equations in function spaces are considered, which depend on perturbation parameters. The nonsmoothness arises from a projection onto an admissible interval. Lipschitz stability in L∞ and Bouligand differentiability in L of the parameter-to-solution map are derived. An adjoint problem is introduced for which Lipschitz stability and Bouligand differentiability in L∞ are obtained. Three different update strategies, which recover a perturbed from an unperturbed solution, are analyzed. They are based on Taylor expansions of the primal and adjoint variables, where the latter admits error estimates in L∞. Numerical results are provided.