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Multigrid Solution of a Lavrentiev-Regularized State-Constrained Parabolic Control Problem

Published online by Cambridge University Press:  28 May 2015

Alfio Borzì  and
Sergio González Andrade
Alfio Borzì*
Affiliation:
Institut für Mathematik, Universität Würzburg, Campus Hubland Nord, Emil-Fischer-Str. 30, 97074 Würzburg, Germany
Sergio González Andrade*
Affiliation:
Research Group on Optimization, Departamento de Matemática, Escuela Politécnica Nacional, Ladrón de Guevara E1 1-253, Quito, Ecuador
*
Corresponding author.Email address:alfio.borzi@mathematik.uni-wuerzburg.de
Corresponding author.Email address:sergio.gonzalez@epn.edu.ec
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Abstract

A mesh-independent, robust, and accurate multigrid scheme to solve a linear state-constrained parabolic optimal control problem is presented. We first consider a Lavrentiev regularization of the state-constrained optimization problem. Then, a multi-grid scheme is designed for the numerical solution of the regularized optimality system. Central to this scheme is the construction of an iterative pointwise smoother which can be formulated as a local semismooth Newton iteration. Results of numerical experiments and theoretical twogrid local Fourier analysis estimates demonstrate that the proposed scheme is able to solve parabolic state-constrained optimality systems with textbook multigrid efficiency.

Keywords

35K1049K2049J2049M0565M5565C20Multigrid methodsLavrentiev regularizationsemismooth Newton methodsparabolic partial differential equationsoptimal control theory
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 1 , February 2012 , pp. 1 - 18
Copyright
Copyright © Global Science Press Limited 2012

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