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A Fast Solver for an H1 Regularized PDE-Constrained Optimization Problem

Published online by Cambridge University Press:  15 January 2016

Andrew T. Barker
Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Mail Stop L-561, Livermore, CA 94551, USA
Tyrone Rees
Numerical Analysis Group, Scientific Computing Department, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, United Kingdom
Martin Stoll
Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
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In this paper we consider PDE-constrained optimization problems which incorporate an H1 regularization control term. We focus on a time-dependent PDE, and consider both distributed and boundary control. The problems we consider include bound constraints on the state, and we use a Moreau-Yosida penalty function to handle this. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.

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A Fast Solver for an H1 Regularized PDE-Constrained Optimization Problem
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