Preconditioned Conjugate Gradient Method for Optimal Control Problems with Control and State Constraints

@article{Herzog2010PreconditionedCG,
  title={Preconditioned Conjugate Gradient Method for Optimal Control Problems with Control and State Constraints},
  author={Roland Herzog and Ekkehard W. Sachs},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2010},
  volume={31},
  pages={2291-2317}
}
Optimality systems and their linearizations arising in optimal control of partial differential equations with pointwise control and (regularized) state constraints are considered. The preconditioned conjugate gradient (PCG) method in a nonstandard inner product is employed for their efficient solution. Preconditioned condition numbers are estimated for problems with pointwise control constraints, mixed control-state constraints, and of Moreau-Yosida penalty type. Numerical results for elliptic… 

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