Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization

Michael Hintermüller

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • 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 - Modélisation Mathématique et Analyse Numérique 35.1 (2001): 129-152. <http://eudml.org/doc/194039>.

@article{Hintermüller2001,
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 - Modélisation Mathématique et Analyse Numérique},
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},
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/194039},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Hintermüller, Michael
TI - Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2001
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/194039
ER -

References

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