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In this paper, nonlinear complementarity problem with P 0 -function is studied. Based on a new parametric nonlinear complementarity function, the problem is approximated by a family of parameterized smooth equations, and a nonmonotone inexact smoothing Newton-type method is presented. At each iteration, the proposed algorithm only needs to solve one system of linear equations inexactly and performs only one nonmonotone line search. It is proved to be convergent globally and superlinearly without strict complementarity at the solution. Moreover, the algorithm has locally quadratic convergence under mild conditions. Numerical results are also reported for the tested problems, which show the effectiveness of the proposed algorithm.

A nonmonotone inexact smoothing Newton-type method for P 0 -NCP based on a parametric complementarity function