Mesh-independence of semismooth Newton methods for Lavrentiev-regularized state constrained nonlinear optimal control problems

Authors:
M. Hintermüller;F. Tröltzsch;I. Yousept
Affiliations:
University of Graz, Institute of Mathematics and Scientific Computing, 8010, Graz, Austria;Technische Universität Berlin, Institut für Mathematik, Str. des 17. Juni 136, 10623, Berlin, Germany;Technische Universität Berlin, Institut für Mathematik, Str. des 17. Juni 136, 10623, Berlin, Germany
Venue:
Numerische Mathematik
Year:
2008

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Abstract

A class of nonlinear elliptic optimal control problems with mixed control-state constraints arising, e.g., in Lavrentiev-type regularized state constrained optimal control is considered. Based on its first order necessary optimality conditions, a semismooth Newton method is proposed and its fast local convergence in function space as well as a mesh-independence principle for appropriate discretizations are proved. The paper ends by a numerical verification of the theoretical results including a study of the algorithm in the case of vanishing Lavrentiev-parameter. The latter process is realized numerically by a combination of a nested iteration concept and an extrapolation technique for the state with respect to the Lavrentiev-parameter.