Nesterov’s accelerated gradient method for nonlinear ill-posed problems with a locally convex residual functional
Publication type: Journal Article
Publication date: 2018-07-12
scimago Q1
wos Q1
SJR: 0.898
CiteScore: 3.3
Impact factor: 2.1
ISSN: 02665611, 13616420
Computer Science Applications
Mathematical Physics
Applied Mathematics
Theoretical Computer Science
Signal Processing
Abstract
In this paper, we consider Nesterov's Accelerated Gradient method for solving Nonlinear Inverse and Ill-Posed Problems. Known to be a fast gradient-based iterative method for solving well-posed convex optimization problems, this method also leads to promising results for ill-posed problems. Here, we provide a convergence analysis for ill-posed problems of this method based on the assumption of a locally convex residual functional. Furthermore, we demonstrate the usefulness of the method on a number of numerical examples based on a nonlinear diagonal operator and on an inverse problem in auto-convolution.
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27
Total citations:
27
Citations from 2024:
9
(33.33%)
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Hubmer S., Ramlau R. Nesterov’s accelerated gradient method for nonlinear ill-posed problems with a locally convex residual functional // Inverse Problems. 2018. Vol. 34. No. 9. p. 95003.
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Hubmer S., Ramlau R. Nesterov’s accelerated gradient method for nonlinear ill-posed problems with a locally convex residual functional // Inverse Problems. 2018. Vol. 34. No. 9. p. 95003.
Cite this
RIS
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TY - JOUR
DO - 10.1088/1361-6420/aacebe
UR - https://doi.org/10.1088/1361-6420/aacebe
TI - Nesterov’s accelerated gradient method for nonlinear ill-posed problems with a locally convex residual functional
T2 - Inverse Problems
AU - Hubmer, Simon
AU - Ramlau, R.
PY - 2018
DA - 2018/07/12
PB - IOP Publishing
SP - 95003
IS - 9
VL - 34
SN - 0266-5611
SN - 1361-6420
ER -
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BibTex (up to 50 authors)
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@article{2018_Hubmer,
author = {Simon Hubmer and R. Ramlau},
title = {Nesterov’s accelerated gradient method for nonlinear ill-posed problems with a locally convex residual functional},
journal = {Inverse Problems},
year = {2018},
volume = {34},
publisher = {IOP Publishing},
month = {jul},
url = {https://doi.org/10.1088/1361-6420/aacebe},
number = {9},
pages = {95003},
doi = {10.1088/1361-6420/aacebe}
}
Cite this
MLA
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Hubmer, Simon, and R. Ramlau. “Nesterov’s accelerated gradient method for nonlinear ill-posed problems with a locally convex residual functional.” Inverse Problems, vol. 34, no. 9, Jul. 2018, p. 95003. https://doi.org/10.1088/1361-6420/aacebe.