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• W2002178240 abstract "This work is concerned with nonlinear parameter identification in partial differential equations subject to impulsive noise. To cope with the non-Gaussian nature of the noise, we consider a model with $mbox{L}^1$ fitting. However, the nonsmoothness of the problem makes its efficient numerical solution challenging. By approximating this problem using a family of smoothed functionals, a semismooth Newton method becomes applicable. In particular, its superlinear convergence is proved under a second-order condition. The convergence of the solution to the approximating problem as the smoothing parameter goes to zero is shown. A strategy for adaptively selecting the regularization parameter based on a balancing principle is suggested. The efficiency of the method is illustrated on several benchmark inverse problems of recovering coefficients in elliptic differential equations, for which one- and two-dimensional numerical examples are presented." @default.
• W2002178240 created "2016-06-24" @default.
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• W2002178240 date "2012-01-01" @default.
• W2002178240 modified "2023-09-27" @default.
• W2002178240 title "A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise" @default.
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• W2002178240 doi "https://doi.org/10.1137/110826187" @default.
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