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

Authors:
M. Hintermüller;I. Kopacka
Affiliations:
Department of Mathematics, Humboldt-University of Berlin, Berlin, Germany 10099 and Department of Mathematics and Scientific Computing, Karl-Franzens-University of Graz, Graz, Austria 8010;Department of Mathematics and Scientific Computing, Karl-Franzens-University of Graz, Graz, Austria 8010
Venue:
Computational Optimization and Applications
Year:
2011

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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.