期刊论文

Zou, Jun

英文

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

0764-583X

2018

52

3

1085-1107

10.1051/m2an/2018016

∗ The work of this author was financially supported by National Natural Science Foundation of China (Nos. 11401241 and 11571265) and NSFC-RGC(China-Hong Kong, No. 11661161017). ∗∗ The work of this author was supported by National Natural Science Foundation of China (No. 91130022, No. 10971159 and No. 11161130003) and The Doctoral Fund of Ministry of Education of China (No. 20130141110026). ∗∗∗ The work of this author was substantially supported by Hong Kong RGC grant (Project 14322516). Corresponding author: zou@math.cuhk.edu.hk

本校为第一机构

We study the Levenberg-Marquardt (L-M) method for solving the highly nonlinear and ill-posed inverse problem of identifying the Robin coefficients in elliptic and parabolic systems. The L-M method transforms the Tikhonov regularized nonlinear non-convex minimizations into convex minimizations. And the quadratic convergence of the L-M method is rigorously established for the nonlinear elliptic and parabolic inverse problems for the first time, under a simple novel adaptive strategy for selecting regularization parameters during the L-M iteration...