Journal of the Operations Research Society of China >

2018 , Vol. 6 >Issue 3: 417 - 428

DOI: https://doi.org/https://doi.org/10.1007/s40305-017-0184-0

Continuous Optimization

Global Complexity Bound of the Inexact Levenberg–Marquardt Method

Expand
  • 1 School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
    2 School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240,China  

Online published: 2018-09-30

Supported by

This work was partially supported by the National Natural Science Foundation of China (No. 11571234).

Fold

Abstract

In this paper, we investigate the global complexity bound for the inexact Levenberg–Marquardt method, where the Jacobian may be perturbed and the solution is possibly not exact. Under reasonable assumptions, we show that the global complexity bound is , which is the same as the exact case. We also show that it can be reduced to under some regularity assumption.

Key words： Global complexity bound ·; Inexact Levenberg–Marquardt method ·Nonlinear equations

Cite this article

Jian-Chao Huang, Jin-Yan Fan .

Global Complexity Bound of the Inexact Levenberg–Marquardt Method
[J]. Journal of the Operations Research Society of China, 2018 , 6(3) : 417 -428 . DOI: https://doi.org/10.1007/s40305-017-0184-0

Options
Outlines

/

〈 〉

Copyright © Operations Research Society of China, The Periodicals Agency of Shanghai University , and Springer-Verlag Berlin Heidelberg 2016