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- W3100740034 abstract "This work is concerned with the iterative regularization of a non-smooth nonlinear ill-posed problem where the forward mapping is merely directionally but not G^ateaux differentiable. Using a Bouligand subderivative of the forward mapping, a modified Landweber method can be applied; however, the standard analysis is not applicable since the Bouligand subderivative mapping is not continuous unless the forward mapping is G^ateaux differentiable. We therefore provide a novel convergence analysis of the modified Landweber method that is based on the concept of asymptotic stability and merely requires a generalized tangential cone condition. These conditions are verified for an inverse source problem for an elliptic PDE with a non-smooth Lipschitz continuous nonlinearity, showing that the corresponding Bouligand--Landweber iteration converges strongly for exact data as well as in the limit of vanishing data if the iteration is stopped according to the discrepancy principle. This is illustrated" @default.
- W3100740034 created "2020-11-23" @default.
- W3100740034 creator A5011665383 @default.
- W3100740034 creator A5058708435 @default.
- W3100740034 date "2019-04-04" @default.
- W3100740034 modified "2023-09-27" @default.
- W3100740034 title "Bouligand–Landweber iteration for a non-smooth ill-posed problem" @default.
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- W3100740034 doi "https://doi.org/10.1007/s00211-019-01038-6" @default.
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