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Majorization-minimization-based Levenberg–Marquardt method for constrained nonlinear least squares

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Bibliographic Details
Main Authors: Naoki, Marumo, Takayuki, Okuno, Akiko, Takeda
Format: Book
Language:English
Published: Springer 2023
Subjects:
Levenberg–Marquardt
LM method
Online Access:https://link.springer.com/article/10.1007/s10589-022-00447-y
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7407
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spelling oai:localhost:PNK-74072023-04-03T01:55:57Z Majorization-minimization-based Levenberg–Marquardt method for constrained nonlinear least squares Naoki, Marumo Takayuki, Okuno Akiko, Takeda Levenberg–Marquardt LM method CC BY A new Levenberg–Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping parameter. In this paper, we propose a new rule for updating the parameter so as to achieve both global and local convergence even under the presence of a convex constraint set. The key to our results is a new perspective of the LM method from majorization-minimization methods. Specifically, we show that if the damping parameter is set in a specific way, the objective function of the standard subproblem in LM methods becomes an upper bound on the original objective function under certain standard assumptions. Our method solves a sequence of the subproblems approximately using an (accelerated) projected gradient method. 2023-04-03T01:55:57Z 2023-04-03T01:55:57Z 2023 Book https://link.springer.com/article/10.1007/s10589-022-00447-y https://dlib.phenikaa-uni.edu.vn/handle/PNK/7407 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic Levenberg–Marquardt
LM method
spellingShingle Levenberg–Marquardt
LM method
Naoki, Marumo
Takayuki, Okuno
Akiko, Takeda
Majorization-minimization-based Levenberg–Marquardt method for constrained nonlinear least squares
description CC BY
format Book
author Naoki, Marumo
Takayuki, Okuno
Akiko, Takeda
author_facet Naoki, Marumo
Takayuki, Okuno
Akiko, Takeda
author_sort Naoki, Marumo
title Majorization-minimization-based Levenberg–Marquardt method for constrained nonlinear least squares
title_short Majorization-minimization-based Levenberg–Marquardt method for constrained nonlinear least squares
title_full Majorization-minimization-based Levenberg–Marquardt method for constrained nonlinear least squares
title_fullStr Majorization-minimization-based Levenberg–Marquardt method for constrained nonlinear least squares
title_full_unstemmed Majorization-minimization-based Levenberg–Marquardt method for constrained nonlinear least squares
title_sort majorization-minimization-based levenberg–marquardt method for constrained nonlinear least squares
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s10589-022-00447-y
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7407
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score 8.881002

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