@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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.190914.080415a},
url = {http://global-sci.org/intro/article_detail/cicp/11083.html}
}