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    A new approach to nonlinear constrained Tikhonov regularization

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    Type
    Article
    Authors
    Ito, Kazufumi
    Jin, Bangti
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2011-09-16
    Online Publication Date
    2011-09-16
    Print Publication Date
    2011-10-01
    Permanent link to this record
    http://hdl.handle.net/10754/597333
    
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    Abstract
    We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of the forward operator. The approach is exploited to derive convergence rate results for a priori as well as a posteriori choice rules, e.g., discrepancy principle and balancing principle, for selecting the regularization parameter. The idea is further illustrated on a general class of parameter identification problems, for which (new) source and nonlinearity conditions are derived and the structural property of the nonlinearity term is revealed. A number of examples including identifying distributed parameters in elliptic differential equations are presented. © 2011 IOP Publishing Ltd.
    Citation
    Ito K, Jin B (2011) A new approach to nonlinear constrained Tikhonov regularization. Inverse Problems 27: 105005. Available: http://dx.doi.org/10.1088/0266-5611/27/10/105005.
    Sponsors
    The authors are grateful to two anonymous referees whose constructive comments have led to an improved presentation. The work of BJ was supported by Award no KUS-C1-016-04, made by the King Abdullah University of Science and Technology (KAUST). A part of the work was carried out during his visit at Graduate School of Mathematical Sciences, The University of Tokyo, and he would like to thank Professor Masahiro Yamamoto for the kind invitation and hospitality.
    Publisher
    IOP Publishing
    Journal
    Inverse Problems
    DOI
    10.1088/0266-5611/27/10/105005
    ae974a485f413a2113503eed53cd6c53
    10.1088/0266-5611/27/10/105005
    Scopus Count
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