Update strategies for perturbed nonsmooth equations

Authors:
Roland Griesse;Thomas Grund;Daniel Wachsmuth
Affiliations:
RICAM, Australian Academy of Sciences, Linz, Austria;Institute of Mechatronics, Chemnitz, Germany;Technische Universitat Berlin, Berlin, Germany
Venue:
Optimization Methods & Software
Year:
2008

Citing 4
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Abstract

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 Lp 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 analysed. They are based on Taylor expansions of the primal and adjoint variables, where the latter admits error estimates in L∞. Numerical results are provided.