Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2014-24

M. Hintermüller, C. Löbhard, and M.H. Tber

An l^1-penalty scheme for the optimal control of elliptic variational inequalities


Abstract: An l^1-penalty scheme in function space for the optimal control of elliptic variational inequalities (VIs) is proposed. In an L2-tracking context, an iterative algorithm is proven to generate a sequence which converges to a Cstationary point and, under certain conditions, even to a strongly stationary point of the original problem. In the case of point tracking control, where the objective contains pointwise function evaluations of the state variable, a modied model problem with constraints on the dual variable associated with the VI constraint is introduced and an auxiliary problem that penalizes not only the complementarity, but also the state constraint, is analyzed. Passing to the limit with the penalty parameter in the stationarity system of the auxiliary problem yields a C-stationarity system for the original problem if the additional dual constraints are not active. Finally, numerical results obtained by the new algorithms are documented.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2014-24


31 pp.