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.
Keywords: bilevel problem, complementarity function, inverse problem, optimal control, variational inequality
@article{M2AN_2001__35_1_129_0,
author = {Hinterm\"uller, Michael},
title = {Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {129--152},
year = {2001},
publisher = {EDP Sciences},
volume = {35},
number = {1},
mrnumber = {1811984},
zbl = {0978.65054},
language = {en},
url = {https://www.numdam.org/item/M2AN_2001__35_1_129_0/}
}
TY - JOUR AU - Hintermüller, Michael TI - Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 129 EP - 152 VL - 35 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/item/M2AN_2001__35_1_129_0/ LA - en ID - M2AN_2001__35_1_129_0 ER -
%0 Journal Article %A Hintermüller, Michael %T Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 129-152 %V 35 %N 1 %I EDP Sciences %U https://www.numdam.org/item/M2AN_2001__35_1_129_0/ %G en %F M2AN_2001__35_1_129_0
Hintermüller, Michael. Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 1, pp. 129-152. https://www.numdam.org/item/M2AN_2001__35_1_129_0/
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