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Volume 19, Issue 1
A Fast Solver for an $\mathcal{H}_1$ Regularized PDE-Constrained Optimization Problem

Andrew T. Barker, Tyrone Rees & Martin Stoll

DOI: 10.4208/cicp.190914.080415a

Commun. Comput. Phys., 19 (2016), pp. 143-167.

Published online: 2018-04

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  • Abstract

In this paper we consider PDE-constrained optimization problems which incorporate an $\mathcal{H}_1$ 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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COPYRIGHT: © Global Science Press

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@Article{CiCP-19-143, author = {Andrew T. Barker, Tyrone Rees and Martin Stoll}, title = {A Fast Solver for an $\mathcal{H}_1$ Regularized PDE-Constrained Optimization Problem}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {1}, pages = {143--167}, abstract = {

In this paper we consider PDE-constrained optimization problems which incorporate an $\mathcal{H}_1$ 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.190914.080415a}, url = {http://global-sci.org/intro/article_detail/cicp/11083.html} }
TY - JOUR T1 - A Fast Solver for an $\mathcal{H}_1$ Regularized PDE-Constrained Optimization Problem AU - Andrew T. Barker, Tyrone Rees & Martin Stoll JO - Communications in Computational Physics VL - 1 SP - 143 EP - 167 PY - 2018 DA - 2018/04 SN - 19 DO - http://doi.org/10.4208/cicp.190914.080415a UR - https://global-sci.org/intro/article_detail/cicp/11083.html KW - AB -

In this paper we consider PDE-constrained optimization problems which incorporate an $\mathcal{H}_1$ 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.

Andrew T. Barker, Tyrone Rees and Martin Stoll. (2018). A Fast Solver for an $\mathcal{H}_1$ Regularized PDE-Constrained Optimization Problem. Communications in Computational Physics. 19 (1). 143-167. doi:10.4208/cicp.190914.080415a
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