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Inverse coefficient problems for variational inequalities: Optimality conditions and numerical realization. (English) Zbl 0978.65054
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.
The discretized first order optimality conditions system is solved by a stabilized Gauss-Newton method. Numerical tests are presented.
Reviewer: V.Arnăutu (Iaşi)

MSC:
65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
49M30 Other numerical methods in calculus of variations (MSC2010)
76D08 Lubrication theory
76M30 Variational methods applied to problems in fluid mechanics
49M15 Newton-type methods
49N45 Inverse problems in optimal control
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