The Mathematical Institute, University of Oxford, Eprints Archive

Robust Iterative Solution of a Class of Time-Dependent Optimal Control Problems

Pearson, John W. and Stoll, Martin and Wathen, A. J. (2012) Robust Iterative Solution of a Class of Time-Dependent Optimal Control Problems. Technical Report. Wiley. (Submitted)

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Abstract

The fast iterative solution of optimal control problems, and in particular PDE-constrained optimization problems, has become an active area of research in applied mathematics and numerical analysis. In this paper, we consider the solution of a class of time-dependent PDE-constrained optimization problems, specifically the distributed control of the heat equation. We develop a strategy to approximate the (1,1)-block and Schur complement of the saddle point system that results from solving this problem, and therefore derive a block diagonal preconditioner to be used within the MINRES algorithm. We present numerical results to demonstrate that this approach yields a robust solver with respect to step-size and regularization parameter.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1560
Deposited By:Lotti Ekert
Deposited On:18 Jul 2012 07:26
Last Modified:18 Jul 2012 07:26

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