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A variant smoothing Newton method for $$P_0$$-$$NCP$$ based on a new smoothing function. (English) Zbl 1163.65043
Recently, there have been strong interests in smoothing Newton methods for solving the non-linear complementarity problems. The idea of smoothing Newton method is to use a smooth function to reformulate the problem concerned as a family of parameterized smooth equations to solve the smooth equations approximately by using the Newton method per iteration. By reducing the parameter to zero, it is hoped that a solution of the original problem can be found.
In this paper, the authors present a new one-step smoothing Newton method proposed for solving the nonlinear complementarity problem (NCP) with $$P_0$$-function based on a new smoothing $$NCP$$-function. They adopt a variant merit function. This algorithm needs only to solve one system of linear equations and performs one line search per iteration. It shows that any accumulation point of the iteration sequence generated by the algorithm is a solution of $$P_0$$-$$NCP$$. Furthermore, under the assumption that the solution set is non-empty and bounded, at least one accumulation point of the generated sequence can be guaranteed. Numerical experiments show the feasibility and efficiency of the algorithm.

MSC:
 65K05 Numerical mathematical programming methods 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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References:
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