Volume 47, Number 3, May-June 2013
|Page(s)||771 - 787|
|Published online||04 March 2013|
Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints∗
1 Konrad-Zuse-Zentrum für
Informationstechnik Berlin (ZIB), Takustraße 7, 14195
2 Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstraße 69, A–4040 Linz, Austria
Revised: 11 September 2012
In the article an optimal control problem subject to a stationary variational inequality is investigated. The optimal control problem is complemented with pointwise control constraints. The convergence of a smoothing scheme is analyzed. There, the variational inequality is replaced by a semilinear elliptic equation. It is shown that solutions of the regularized optimal control problem converge to solutions of the original one. Passing to the limit in the optimality system of the regularized problem allows to prove C-stationarity of local solutions of the original problem. Moreover, convergence rates with respect to the regularization parameter for the error in the control are obtained, which turn out to be sharp. These rates coincide with rates obtained by numerical experiments, which are included in the paper.
Mathematics Subject Classification: 49K20 / 65K15 / 49M20 / 90C33
Key words: Variational inequalities / optimal control / control constraints / regularization / C-stationarity / path-following
© EDP Sciences, SMAI, 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.