Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities

@article{Chen1998GlobalAS,
title={Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities},
author={Xiaojun Chen and Liqun Qi and Defeng Sun},
journal={Math. Comput.},
year={1998},
volume={67},
pages={519-540}
}

The smoothing Newton method for solving a system of nonsmooth equations F (x) = 0, which may arise from the nonlinear complementarity problem, the variational inequality problem or other problems, can be regarded as a variant of the smoothing method. At the kth step, the nonsmooth function F is approximated by a smooth function f(·, εk), and the derivative of f(·, εk) at xk is used as the Newton iterative matrix. The merits of smoothing methods and smoothing Newton methods are global… CONTINUE READING