Preconditioners for state‐constrained optimal control problems with Moreau–Yosida penalty function |
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Authors: | John W. Pearson Martin Stoll Andrew J. Wathen |
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Affiliation: | 1. Numerical Analysis Group, Mathematical Institute, , Oxford, OX1 3LB U.K.;2. Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, , 39106 Magdeburg, Germany |
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Abstract: | Optimal control problems with partial differential equations as constraints play an important role in many applications. The inclusion of bound constraints for the state variable poses a significant challenge for optimization methods. Our focus here is on the incorporation of the constraints via the Moreau–Yosida regularization technique. This method has been studied recently and has proven to be advantageous compared with other approaches. In this paper, we develop robust preconditioners for the efficient solution of the Newton steps associated with the fast solution of the Moreau–Yosida regularized problem. Numerical results illustrate the efficiency of our approach. Copyright © 2012 John Wiley & Sons, Ltd. |
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Keywords: | state‐constrained problems PDE‐constrained optimization saddle point systems preconditioning Newton method Krylov subspace solver |
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