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

Michael Hintermüller

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

Abstract

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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.

How to cite

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Hintermüller, 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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