Convergence rate of the modified Levenberg-Marquardt method under Hölderian local error bound-Reference-Cited by-同舟云学术

Convergence rate of the modified Levenberg-Marquardt method under Hölderian local error bound

Published:2022-01-01 Issue:1 Volume:20 Page:998-1012
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Zheng Lin¹²,Chen Liang³,Tang Yangxin¹²

Affiliation:

1. School of Statistics and Applied Mathematics, Anhui University of Finance and Economics , Bengbu 233030 , China

2. Institute of Quantitative Economics, Anhui University of Finance and Economics , Bengbu 233030 , China

3. School of Sciences, Changzhou Institute of Technology , Changzhou , Jiangsu 213032 , China

Abstract

Abstract In this article, we analyze the convergence rate of the modified Levenberg-Marquardt (MLM) method under the Hölderian local error bound condition and the Hölderian continuity of the Jacobian, which are more general than the local error bound condition and the Lipschitz continuity of the Jacobian. Under special circumstances, the convergence rate of the MLM method coincides with the results presented by Fan. A globally convergent MLM algorithm by the trust region technique will also be given.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2022-0485/pdf

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