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Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints

Title data

Schiela, Anton ; Wachsmuth, Daniel:
Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints.
In: ESAIM : Mathematical Modelling and Numerical Analysis. Vol. 47 (2013) Issue 3 . - pp. 771-787.
ISSN 0764-583X
DOI: https://doi.org/10.1051/m2an/2012049

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Project information

Project title:
Project's official titleProject's id
DFG Research Center Matheon "Mathematics for key technologies"FZT 86

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: A preliminary version is published under the title "Convergence Analysis of Smoothing Methods for Optimal Control of Stationary Variational Inequalities" at the Konrad-Zuse-Zentrum für Informationstechnik, Berlin as ZIB-Report 11-23.
Keywords: variational inequalities; optimal control; control constraints; regularization; C-stationarity; path-following
Subject classification: Mathematics Subject Classification Code: 49K20 (65K15 49M20 90C33)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics) > Professorship Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton Schiela
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 17 Mar 2015 10:26
Last Modified: 17 Mar 2015 10:26
URI: https://eref.uni-bayreuth.de/id/eprint/8206