Abstract
An optimal control problem governed by an elliptic variational inequality of the first kind and bilateral control constraints is studied. A smooth penalization technique for the variational inequality is applied and convergence of stationary points of the subproblems to an E-almost C-stationary point of the limit problem is shown. The subproblems are solved using a full approximation multigrid scheme (FAS) and alternatively a multigrid method of the second kind for which a convergence result is given. An overall algorithmic concept is provided and its performance is discussed by means of examples.
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Hintermüller, M., Kopacka, I. A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs. Comput Optim Appl 50, 111–145 (2011). https://doi.org/10.1007/s10589-009-9307-9
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DOI: https://doi.org/10.1007/s10589-009-9307-9