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

Please always quote using this URN:urn:nbn:de:0296-matheon-10355
  • 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.

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Metadaten
Author:Anton Schiela, Daniel Wachsmuth
URN:urn:nbn:de:0296-matheon-10355
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/01/30
Release Date:2012/01/30
Tag:
Institute:Zuse Institute Berlin (ZIB)
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M20 Methods of relaxation type
65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K15 Numerical methods for variational inequalities and related problems
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions)
Preprint Number:901
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