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

ABSTRACT

In this paper, we study the convergence rate of the Levenberg-Marquardt (LM) 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. Various choices of the LM parameter are also discussed.

KEYWORDS:

• Nonlinear equations
• Levenberg-Marquardt method
• Hölderian local error bound
• convergence rate

2000 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65K05
• 90C30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors are supported by National Natural Science Foundation of China (Chinese NSF) grants 11571234 and 11971309.

Notes on contributors

Haiyan Wang

Haiyan Wang is a PhD student at Shanghai Jiao Tong University. She works on numercial methods for nonlinear equations.

Jinyan Fan

Jinyan Fan is a professor of optimization at Shanghai Jiao Tong University. Currently she focuses on numerical methods for nonlinear least squares and tensor optimization.