A partially smoothing Jacobian method for nonlinear complementarity problems with P0 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 P 0 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.

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