Convergence properties of inexact Levenberg-Marquardt method under Hölderian local error bound

Haiyan Wang; Jinyan Fan

doi:10.3934/jimo.2020068

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2021, Volume 17, Issue 4: 2265-2275. Doi: 10.3934/jimo.2020068

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Convergence properties of inexact Levenberg-Marquardt method under Hölderian local error bound

Haiyan Wang^1, and
Jinyan Fan^2, ,

1.
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
2.
School of Mathematical Sciences, Shanghai Jiao Tong University, Key Lab of Scientific and Engineering Computing (Ministry of Education), Shanghai 200240, China

^* Corresponding author: Jinyan Fan
^* Corresponding author: Jinyan Fan

Received: July 31, 2019

Revised: October 31, 2019

Early access: March 2020

Published: July 2021

The authors are supported by Chinese NSF grants 11971309

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Abstract

In this paper, we study convergence properties of the inexact Levenberg-Marquardt method under the Hölderian local error bound condition and the Hölderian continuity of the Jacobian. The formula of the convergence rates are given, which are functions with respect to the Levenberg-Marquardt parameter, the perturbation vector, as well as the orders of the Hölderian local error bound and Hölderian continuity of the Jacobian.

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Mathematics Subject Classification: 65K05, 90C30.

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