A smoothing Newton method for general nonlinear complementarity problems

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.