Smoothing Newton methods for nonlinear complementarity problems NCP(F) ofte
n require F to be at least a P-0-function in order to guarantee that the un
derlying Newton equation is solvable. Based on a special equation reformula
tion of NCP(F), we propose a new smoothing Newton method for general nonlin
ear complementarity problems. The introduction of Kanzow and Pieper's gradi
ent step makes our algorithm to be globally convergent. Under certain condi
tions, our method achieves fast local convergence rate. Extensive numerical
results are also reported for all complementarity problems in MCPLIB and G
AMSLIB libraries with all available starting points.