Global Complexity Bound of the Inexact Levenberg–Marquardt Method

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

Journal of the Operations Research Society of China ›› 2018, Vol. 6 ›› Issue (3): 417-428.doi: https://doi.org/10.1007/s40305-017-0184-0

所属专题： Continuous Optimization

出版日期:2018-09-30 发布日期:2018-09-30

Global Complexity Bound of the Inexact Levenberg–Marquardt Method

Jian-Chao Huang¹ , Jin-Yan Fan^1,2

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:2018-09-30 Published:2018-09-30
Supported by:
This work was partially supported by the National Natural Science Foundation of China (No. 11571234).

摘要/Abstract

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 $O (ε^{- 2})$ , which is the same as the exact case. We also show that it can be reduced to $O (l g ε^{- 1})$ under some regularity assumption.

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

. [J]. Journal of the Operations Research Society of China, 2018, 6(3): 417-428.

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.

Global Complexity Bound of the Inexact Levenberg–Marquardt Method

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

编辑推荐

Metrics

本文评价