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Robust iterative solution of a class of time-dependent optimal control problems

Pearson, John W and Stoll, Martin and Wathen, Andrew J (2012) Robust iterative solution of a class of time-dependent optimal control problems. In: Proceedings in Applied Mathematics and Mechanics. Wiley, pp. 3-6. (doi:10.1002/pamm.201210002) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1002/pamm.201210002

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: Book section
DOI/Identification number: 10.1002/pamm.201210002
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: John Pearson
Date Deposited: 30 Apr 2015 16:11 UTC
Last Modified: 29 May 2019 14:28 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/48152 (The current URI for this page, for reference purposes)
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