A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities

@article{Qi2000ANL,
title={A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities},
author={Liqun Qi and Defeng Sun and Guanglu Zhou},
journal={Math. Program.},
year={2000},
volume={87},
pages={1-35}
}

In this paper we take a new look at smoothing Newton methods for solving the nonlinear complementarity problem (NCP) and the box constrained variational inequalities (BVI). Instead of using an infinite sequence of smoothing approximation functions, we use a single smoothing approximation function and Robinson’s normal equation to reformulate NCP and BVI as an equivalent nonsmooth equation H(u, x) = 0, whereH : <2n → <2n, u ∈ <n is a parameter variable and x ∈ <n is the original variable. The… CONTINUE READING

Smoothed Fischer-Burmeister equation methods for the nonlinear complementarity problem. Preprint, Department of Mathematics & Statistics, the University of Melbourne, Victoria 3052