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

- 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 - 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 -

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