Geodesic
Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 1, pp. 129-152

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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.

Classification : 49N50, 35R30, 35J85
Keywords: bilevel problem, complementarity function, inverse problem, optimal control, variational inequality 
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     author = {Hinterm\"uller, Michael},
     title = {Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {129--152},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {1},
     year = {2001},
     mrnumber = {1811984},
     zbl = {0978.65054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_129_0/}
}
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Hintermüller, Michael. Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 1, pp. 129-152. http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_129_0/