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Inverse Coefficient Problems for Variational Inequalities: Optimality Conditions and Numerical Realization

Published online by Cambridge University Press:  15 April 2002

Michael Hintermüller
Michael Hintermüller*
Affiliation:
Karl-Franzens University of Graz, Department of Mathematics, Heinrichstraße 36, 8010 Graz, Austria. (michael.hintermueller@kfunigraz.ac.at)
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Abstract

We consider the identification of a distributed parameter in an elliptic variational inequality. On the basis of an optimal control problem formulation, the application of a primal-dual penalization technique enables us to prove the existence of multipliers giving a first order characterization of the optimal solution. Concerning the parameter we consider different regularity requirements. For the numerical realization we utilize a complementarity function, which allows us to rewrite the optimality conditions as a set of equalities. Finally, numerical results obtained from a least squares type algorithm emphasize the feasibility of our approach.

Keywords

Bilevel problemcomplementarity functioninverse problemoptimal controlvariational inequality.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 1 , January 2001 , pp. 129 - 152
Copyright
© EDP Sciences, SMAI, 2001

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