A Smoothing Inexact Newton Method for Nonlinear Complementarity Problems

A smoothing inexact Newton method is presented for solving nonlinear complementarity problems. Different from the existing exact methods, the associated subproblems are not necessary to be exactly solved to obtain the search directions. Under suitable assumptions, global convergence and superlinear convergence are established for the developed inexact algorithm, which are extensions of the exact case. On the one hand, results of numerical experiments indicate that our algorithm is effective for the benchmark test problems available in the literature. On the other hand, suitable choice of inexact parameters can improve the numerical performance of the developed algorithm.