## The convergence of a one-step smoothing Newton method for $$P_0$$-NCP based on a new smoothing NCP-function.(English)Zbl 1140.65046

Authors’ summary: The nonlinear complementarity problem (denoted by NCP$$(F))$$ can be reformulated as the solution of a nonsmooth system of equations. By introducing a new smoothing NCP-function, the problem is approximated by a family of parameterized smooth equations. A one-step smoothing Newton method is proposed for solving the nonlinear complementarity problem with $$P_{0}$$-function ($$P_{0}$$-NCP) based on the new smoothing NCP-function. The proposed algorithm solves only one linear system of equations and performs only one line search per iteration. Without requiring strict complementarity assumption at the $$P_{0}$$-NCP solution, the proposed algorithm is proved to be convergent globally and superlinearly under suitable assumptions. Furthermore, the algorithm has local quadratic convergence under mild conditions.

### 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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