Convergence Analysis of Smoothing Methods for Optimal Control of Stationary Variational Inequalities

Please always quote using this URN: urn:nbn:de:0297-zib-13125

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. These rates coincide with rates obtained by numerical experiments, which are included in the paper.

Metadaten
Author:	Anton Schiela, Daniel Wachsmuth
Document Type:	ZIB-Report
Tag:	C-stationarity; Variational inequalities; control constraints; optimal control; path-following
MSC-Classification:	49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
	65-XX NUMERICAL ANALYSIS
	90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
Date of first Publication:	2011/06/16
Series (Serial Number):	ZIB-Report (11-23)
ZIB-Reportnumber:	11-23

Open Access