Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function
| dc.contributor.author | Pearson, John W. | |
| dc.contributor.author | Stoll, Martin | |
| dc.contributor.author | Wathen, Andrew J. | |
| dc.date.accessioned | 2016-02-28T05:49:55Z | |
| dc.date.available | 2016-02-28T05:49:55Z | |
| dc.date.issued | 2012-11-21 | |
| dc.identifier.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. | |
| dc.identifier.issn | 1070-5325 | |
| dc.identifier.doi | 10.1002/nla.1863 | |
| dc.identifier.uri | http://hdl.handle.net/10754/599377 | |
| dc.description.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. | |
| dc.description.sponsorship | 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). | |
| dc.publisher | Wiley | |
| dc.subject | Krylov subspace solver | |
| dc.subject | Newton method | |
| dc.subject | PDE-constrained optimization | |
| dc.subject | Preconditioning | |
| dc.subject | Saddle point systems | |
| dc.subject | State-constrained problems | |
| dc.title | Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function | |
| dc.type | Article | |
| dc.identifier.journal | Numerical Linear Algebra with Applications | |
| dc.contributor.institution | Numerical Analysis Group; Mathematical Institute; 24-29 St Giles' Oxford OX1 3LB U.K. | |
| dc.contributor.institution | Computational Methods in Systems and Control Theory; Max Planck Institute for Dynamics of Complex Technical Systems; Sandtorstr. 1 39106 Magdeburg Germany | |
| kaust.grant.number | KUK-C1-013-04 | |
| dc.date.published-online | 2012-11-21 | |
| dc.date.published-print | 2014-01 |