In this paper, a smoothing homotopy method for solving the nonlinear complementarity problem is considered. The homotopy equation is constructed based on Chen-Harker-Kanzow-Smale smooth function. Under certain mild nonmonotone condition, the global convergence result is obtained. Furthermore, the initial point can be chosen almost everywhere in $R^n$ but not just in $R^n_+$. The numerical experimental results show that the method is effective.
Xiaona Fan. Tingting Xu. Furong Gao. "SOLVING NONLINEAR COMPLEMENTARITY PROBLEM BY A SMOOTHING HOMOTOPY METHOD." Taiwanese J. Math. 19 (1) 51 - 63, 2015. https://doi.org/10.11650/tjm.19.2015.3357