Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function

Handle URI:
http://hdl.handle.net/10754/599377
Title:
Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function
Authors:
Pearson, John W.; Stoll, Martin; Wathen, Andrew J.
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. © 2012 John Wiley & Sons, Ltd.
Citation:
Pearson JW, Stoll M, Wathen AJ (2012) Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function. Numerical Linear Algebra with Applications 21: 81–97. Available: http://dx.doi.org/10.1002/nla.1863.
Publisher:
Wiley-Blackwell
Journal:
Numerical Linear Algebra with Applications
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
21-Nov-2012
DOI:
10.1002/nla.1863
Type:
Article
ISSN:
1070-5325
Sponsors:
The authors would like to thank the anonymous referees for their careful reading of the manuscript and helpful comments. The authors would also like to thank Anton Schiela for useful conversations about this work. The first author was supported for this work by the Engineering and Physical Sciences Research Council (UK), Grant EP/P505216/1. This publication is partially based on work performed when the second author was supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorPearson, John W.en
dc.contributor.authorStoll, Martinen
dc.contributor.authorWathen, Andrew J.en
dc.date.accessioned2016-02-28T05:49:55Zen
dc.date.available2016-02-28T05:49:55Zen
dc.date.issued2012-11-21en
dc.identifier.citationPearson JW, Stoll M, Wathen AJ (2012) Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function. Numerical Linear Algebra with Applications 21: 81–97. Available: http://dx.doi.org/10.1002/nla.1863.en
dc.identifier.issn1070-5325en
dc.identifier.doi10.1002/nla.1863en
dc.identifier.urihttp://hdl.handle.net/10754/599377en
dc.description.abstractOptimal 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. © 2012 John Wiley & Sons, Ltd.en
dc.description.sponsorshipThe authors would like to thank the anonymous referees for their careful reading of the manuscript and helpful comments. The authors would also like to thank Anton Schiela for useful conversations about this work. The first author was supported for this work by the Engineering and Physical Sciences Research Council (UK), Grant EP/P505216/1. This publication is partially based on work performed when the second author was supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherWiley-Blackwellen
dc.subjectKrylov subspace solveren
dc.subjectNewton methoden
dc.subjectPDE-constrained optimizationen
dc.subjectPreconditioningen
dc.subjectSaddle point systemsen
dc.subjectState-constrained problemsen
dc.titlePreconditioners for state-constrained optimal control problems with Moreau-Yosida penalty functionen
dc.typeArticleen
dc.identifier.journalNumerical Linear Algebra with Applicationsen
dc.contributor.institutionNumerical Analysis Group; Mathematical Institute; 24-29 St Giles' Oxford OX1 3LB U.K.en
dc.contributor.institutionComputational Methods in Systems and Control Theory; Max Planck Institute for Dynamics of Complex Technical Systems; Sandtorstr. 1 39106 Magdeburg Germanyen
kaust.grant.numberKUK-C1-013-04en
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