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Levenberg–Marquardt method for ill-posed inverse problems with possibly non-smooth forward mappings between Banach spaces

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Main Author: Vu, Huu Nhu
Format: Bài báo khoa học
Language:English
Published: Ipop Science 2022
Subjects:
Mapping
Space
Online Access:https://dlib.phenikaa-uni.edu.vn/handle/PNK/4021
https://doi.org/10.1088/1361-6420/ac38b7
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spelling oai:localhost:PNK-40212022-08-17T05:54:49Z Levenberg–Marquardt method for ill-posed inverse problems with possibly non-smooth forward mappings between Banach spaces Vu, Huu Nhu Mapping Space 1, 38 In this paper, we consider a Levenberg–Marquardt method with general regularization terms that are uniformly convex on bounded sets to solve the ill-posed inverse problems in Banach spaces, where the forward mapping might not Gâteaux differentiable and the image space is unnecessarily reflexive. The method therefore extends the one proposed by Jin and Yang in (2016 Numer. Math. 133 655–684) for smooth inverse problem setting with globally uniformly convex regularization terms. We prove a novel convergence analysis of the proposed method under some standing assumptions, in particular, the generalized tangential cone condition and a compactness assumption. All these assumptions are fulfilled when investigating the identification of the heat source for semilinear elliptic boundary-value problems with a Robin boundary condition, a heat source acting on the boundary, and a possibly non-smooth nonlinearity. Therein, the Clarke subdifferential of the non-smooth nonlinearity is employed to construct the family of bounded operators that is a replacement for the non-existing Gâteaux derivative of the forward mapping. The efficiency of the proposed method is illustrated with a numerical example. 2022-01-17T02:27:20Z 2022-01-17T02:27:20Z 2021 Bài báo khoa học https://dlib.phenikaa-uni.edu.vn/handle/PNK/4021 https://doi.org/10.1088/1361-6420/ac38b7 en Ipop Science
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic Mapping
Space
spellingShingle Mapping
Space
Vu, Huu Nhu
Levenberg–Marquardt method for ill-posed inverse problems with possibly non-smooth forward mappings between Banach spaces
description 1, 38
format Bài báo khoa học
author Vu, Huu Nhu
author_facet Vu, Huu Nhu
author_sort Vu, Huu Nhu
title Levenberg–Marquardt method for ill-posed inverse problems with possibly non-smooth forward mappings between Banach spaces
title_short Levenberg–Marquardt method for ill-posed inverse problems with possibly non-smooth forward mappings between Banach spaces
title_full Levenberg–Marquardt method for ill-posed inverse problems with possibly non-smooth forward mappings between Banach spaces
title_fullStr Levenberg–Marquardt method for ill-posed inverse problems with possibly non-smooth forward mappings between Banach spaces
title_full_unstemmed Levenberg–Marquardt method for ill-posed inverse problems with possibly non-smooth forward mappings between Banach spaces
title_sort levenberg–marquardt method for ill-posed inverse problems with possibly non-smooth forward mappings between banach spaces
publisher Ipop Science
publishDate 2022
url https://dlib.phenikaa-uni.edu.vn/handle/PNK/4021
https://doi.org/10.1088/1361-6420/ac38b7
_version_ 1751856272223764480
score 8.891145

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