Show simple item record

dc.contributor.authorStoll, Martin
dc.contributor.authorWathen, Andy
dc.date.accessioned2016-02-28T05:49:59Z
dc.date.available2016-02-28T05:49:59Z
dc.date.issued2011-10-18
dc.identifier.citationStoll M, Wathen A (2011) Preconditioning for partial differential equation constrained optimization with control constraints. Numerical Linear Algebra with Applications 19: 53–71. Available: http://dx.doi.org/10.1002/nla.823.
dc.identifier.issn1070-5325
dc.identifier.doi10.1002/nla.823
dc.identifier.urihttp://hdl.handle.net/10754/599380
dc.description.abstractOptimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal-dual active set method is used. We also show for this method that the same saddle point system can be derived when the method is considered as a semismooth Newton method. In addition, the projected gradient method can be employed to solve optimization problems with simple bounds, and we discuss the efficient solution of the linear systems in question. In the case when an acceleration technique is employed for the projected gradient method, this again yields a semismooth Newton method that is equivalent to the primal-dual active set method. We also consider the Moreau-Yosida regularization method for control constraints and efficient preconditioners for this technique. Numerical results illustrate the competitiveness of these approaches. © 2011 John Wiley & Sons, Ltd.
dc.description.sponsorshipThe first author would like to thank Tyrone Rees and Nick Gould for sharing their knowledge. The authors would also like to thank the anonymous referee for helping to improve this publication. This publication is partially based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
dc.publisherWiley
dc.subjectKrylov subspace solver
dc.subjectNewton method
dc.subjectPDE-constrained optimization
dc.subjectPreconditioning
dc.subjectSaddle point systems
dc.titlePreconditioning for partial differential equation constrained optimization with control constraints
dc.typeArticle
dc.identifier.journalNumerical Linear Algebra with Applications
dc.contributor.institutionOxford Centre for Collaborative Applied Mathematics; Mathematical Institute; 24-29 St Giles'; Oxford; OX1 3LB; U.K.
dc.contributor.institutionNumerical Analysis Group; Mathematical Institute; 24-29 St Giles'; Oxford; OX1 3LB; U.K.
kaust.grant.numberKUK-C1-013-04
dc.date.published-online2011-10-18
dc.date.published-print2012-01


This item appears in the following Collection(s)

Show simple item record