# American Institute of Mathematical Sciences

July  2021, 17(4): 2265-2275. doi: 10.3934/jimo.2020068

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

 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

Received  August 2019 Revised  November 2019 Published  March 2020

Fund Project: The authors are supported by Chinese NSF grants 11971309

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.

Citation: Haiyan Wang, Jinyan Fan. Convergence properties of inexact Levenberg-Marquardt method under Hölderian local error bound. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2265-2275. doi: 10.3934/jimo.2020068
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