Update strategies for perturbed nonsmooth equations
Non smooth 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-infinity and Bouligand differentiability in L-p of the paraineter-to-solution map are derived. An adjoint problem is introduced for which Lipschitz stability and Bouligand differentiability in L-infinity are obtained. Three different update strategies, which recover a Perturbed from an unperturbed solution, are analysed. They are based on Taylor expansions of the primal and adjoint variables, where the latter admits error estimates in L-infinity. Numerical results are provided.
nonsmooth equation taylor expansion variational inequality bouligand derivative optimal control