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A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs

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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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Authors and Affiliations

  1. Department of Mathematics, Humboldt-University of Berlin, Unter den Linden 6, 10099, Berlin, Germany

    M. Hintermüller

  2. Department of Mathematics and Scientific Computing, Karl-Franzens-University of Graz, Heinrichstrasse 36, 8010, Graz, Austria

    M. Hintermüller & I. Kopacka

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  1. M. Hintermüller
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  2. I. Kopacka
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Correspondence to M. Hintermüller.

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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

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