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A new one-step smoothing Newton method for nonlinear complementarity problem with \(P_{0}\)-function. (English) Zbl 1239.65034
Summary: A nonlinear complementarity problem with \(P_{0}\)-function is studied. Based on a new smoothing function, the problem is approximated by a family of parameterized smooth equations and we present a new one-step smoothing Newton method to solve it. At each iteration, the proposed method only need to solve one system of linear equations and perform one Armijo-type line search. The algorithm is proved to be convergent globally and superlinearly without requiring strict complementarity at the solution. Numerical experiments demonstrate the feasibility and efficiency of the new 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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