TY - JOUR
T1 - A Parameter-Self-Adjusting Levenberg-Marquardt Method for Solving Nonsmooth Equations
AU - Qi , Liyan
AU - Xiao , Xiantao
AU - Zhang , Liwei
JO - Journal of Computational Mathematics
VL - 3
SP - 317
EP - 338
PY - 2016
DA - 2016/06
SN - 34
DO - http://doi.org/10.4208/jcm.1512-m2015-0333
UR - https://global-sci.org/intro/article_detail/jcm/9798.html
KW - Levenberg-Marquardt method, Nonsmooth equations, Nonlinear complementarity problems.
AB - <p style="text-align: justify;">A parameter-self-adjusting Levenberg-Marquardt method (PSA-LMM) is proposed for solving a nonlinear system of equations $F(x) = 0$, where $F : \mathbb{R}^n$ →$\mathbb{R}^n$ is a semismooth mapping. At each iteration, the LM parameter $μ_k$ is automatically adjusted based on the ratio between actual reduction and predicted reduction. The global convergence of PSA-LMM for solving semismooth equations is demonstrated. Under the BD-regular condition, we prove that PSA-LMM is locally superlinearly convergent for semismooth equations and locally quadratically convergent for strongly semismooth equations. Numerical results for solving nonlinear complementarity problems are presented.</p>