Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems

@article{Pearson2012RegularizationRobustPF,
  title={Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems},
  author={John W. Pearson and M. Stoll and Andrew J. Wathen},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2012},
  volume={33},
  pages={1126-1152}
}
In this article, we motivate, derive, and test effective preconditioners to be used with the Minres algorithm for solving a number of saddle point systems which arise in PDE-constrained optimization problems. We consider the distributed control problem involving the heat equation and the Neumann boundary control problem involving Poisson's equation and the heat equation. Crucial to the effectiveness of our preconditioners in each case is an effective approximation of the Schur complement of the… 
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