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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 35, Issue: 1, page 129-152
- ISSN: 0764-583X

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topHintermüller, Michael. "Inverse Coefficient Problems for Variational Inequalities: Optimality Conditions and Numerical Realization." ESAIM: Mathematical Modelling and Numerical Analysis 35.1 (2010): 129-152. <http://eudml.org/doc/197552>.

@article{Hintermüller2010,

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.
},

author = {Hintermüller, Michael},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Bilevel problem; complementarity function; inverse problem; optimal control; variational inequality.; elliptic variational inequality; inverse elastohydrodynamic lubrication problem; least squares method; primal-dual penalization technique; complementarity functions; algorithm; Gauss-Newton method; numerical tests},

language = {eng},

month = {3},

number = {1},

pages = {129-152},

publisher = {EDP Sciences},

title = {Inverse Coefficient Problems for Variational Inequalities: Optimality Conditions and Numerical Realization},

url = {http://eudml.org/doc/197552},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Hintermüller, Michael

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 35

IS - 1

SP - 129

EP - 152

AB -
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.

LA - eng

KW - Bilevel problem; complementarity function; inverse problem; optimal control; variational inequality.; elliptic variational inequality; inverse elastohydrodynamic lubrication problem; least squares method; primal-dual penalization technique; complementarity functions; algorithm; Gauss-Newton method; numerical tests

UR - http://eudml.org/doc/197552

ER -

## References

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