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

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    Type
    Article
    Authors
    Pearson, John W.
    Stoll, Martin
    Wathen, Andrew J.
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2012-11-21
    Online Publication Date
    2012-11-21
    Print Publication Date
    2014-01
    Permanent link to this record
    http://hdl.handle.net/10754/599377
    
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    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.
    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).
    Publisher
    Wiley
    Journal
    Numerical Linear Algebra with Applications
    DOI
    10.1002/nla.1863
    ae974a485f413a2113503eed53cd6c53
    10.1002/nla.1863
    Scopus Count
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