A partially smoothing Jacobian method for nonlinear complementarity problems with P0P0 function

In this paper, we propose a partially smoothing function for solving the nonlinear complementarity problems (NCP). Some properties of such a smoothing approach are analyzed and are employed to develop a well defined and efficient Jacobian Newton algorithm to find the solution of NCP. Under the condition that the level set of a merit function is bounded, global convergence and super-linear convergence are established for the developed algorithm. Compared with the similar theoretical results available in the literature, the assumption of nonsingularity is removed in virtue of P0P0 property and the smoothing approach. Numerical experiments show that the proposed smoothing method outperforms the existent ones, particularly in comparison with the state-of-art methods derived from the classical Fischer–Burmeister smoothing function and the aggregation function.