The modulus-based nonsmooth Newton’s method for solving a class of nonlinear complementarity problems of <Emphasis Type="Italic">P</Emphasis>-matrices

By applying the Newton’s iteration to the equivalent modulus equations of the nonlinear complementarity problems of P-matrices, a modulus-based nonsmooth Newton’s method is established. The nearly quadratic convergence of the new method is proved under some assumptions. The strategy of choosing the initial iteration vector is given, which leads to a modified method. Numerical examples show that the new methods have higher convergence precision and faster convergence rate than the known modulus-based matrix splitting iteration method.