A smooth Newton method with 3-1 piecewise NCP function for generalized nonlinear complementarity problem.

In this paper, based on the 3-1 piecewise nonlinear complementarity problem (NCP) function, we proposed a smoothing Newton-type method for the generalized nonlinear complementarity problem (GNCP) with a modified non-monotone line search. The algorithm for a GNCP is more difficult than that for an NCP, because two functions must be considered in the problem. We reformulate the (GNCP) to a smoothing system of equations by two independent variables, and then develop a smoothing Newton-type method for solving it. Under reasonable conditions, we obtain the global convergent properties. Also, the numerical experiments are reported in this paper. [ABSTRACT FROM AUTHOR]