@article{0978.65054,
author="Hinterm\"uller, Michael",
title="{Inverse coefficient problems for variational inequalities: Optimality
    conditions and numerical realization.}",
language="English",
year="2001",
doi={10.1051/m2an:2001109},
abstract="{The identification of a distributed parameter in an elliptic
    variational inequality is considered. A practical application is the inverse
    elastohydrodynamic lubrication problem. Using the least squares method leads
    to a bilevel optimal control problem. The classical Lagrange multipliers
    approach fails. The author uses a primal-dual penalization technique. The
    optimality system for the optimal control problem, which is derived on the
    basis of this penalization technique, and the use of the concept of
    complementarity functions lead to a numerical algorithm. \par The
    discretized first order optimality conditions system is solved by a
    stabilized Gauss-Newton method. Numerical tests are presented.}",
reviewer="{V.Arn\u{a}utu (Ia\c{s}i)}",
keywords="{inverse problem; elliptic variational inequality; inverse
    elastohydrodynamic lubrication problem; least squares method; optimal
    control; primal-dual penalization technique; complementarity functions;
    algorithm; Gauss-Newton method; numerical tests}",
classmath="{*65K10 (Optimization techniques (numerical methods))
49J40 (Variational methods including variational inequalities)
49M30 (Methods of successive approximation, not based on necessary cond.)
76D08 (Lubrication theory)
76M30 (Variational methods)
49M15 (Methods of Newton-Raphson, Galerkin and Ritz types)
49N45 (Inverse problems in calculus of variations)
}",
}