@article{pre05291920,
author="Hinterm\"uller, M.",
title="{An active-set equality constrained Newton solver with feasibility
restoration for inverse coefficient problems in elliptic variational
inequalities.}",
language="English",
year="2008",
doi={10.1088/0266-5611/24/3/034017},
abstract="{Summary: An output-least-squares formulation for a class of parameter
identification problems for elliptic variational inequalities is considered.
Based on the concept of C-stationarity an active set type solver with
feasibility restoration is introduced. It is shown that the new method
relates to the so-called implicit programming techniques in the context of
mathematical programs with equilibrium constraints. In the discrete setting,
in order to overcome the ill-posedness of the problem, the parameter of
interest is discretized on a coarser mesh than the state of the system. In
addition, if the parameter corresponds to the coefficient in the bilinear
form of the underlying differential operator, an interior-point treatment is
employed to maintain the coercivity of the elliptic operator. Moreover, the
computational domain for the coefficient depends on the measurement data.
The paper ends with a report on numerical tests including an application to
a simplified lubrication problem in a rolling element device.}",
classmath="{*35R30 (Inverse problems for PDE)
35J85 (Unilateral problems; variational inequalities (elliptic type))
65N21 (Inverse problems)
90-99 (Optimization)
}",
}