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The quadratic convergence of a smoothing Levenberg-Marquardt method for nonlinear complementarity problem. (English) Zbl 1141.65044
The authors approximate the problem of the least $${l}_2$$-norm solution of the equivalent nonsmooth equations of a nonlinear complementarity problem with a family of parameterized twice smooth optimization problem by making use of a new smoothing function. A smoothing Levenberg-Marquardt method is presented to solve the parameterized smooth optimization problem. The proposed method is shown to be globally convergent under an assumption that the level set of the problem is compact. By making use of the smooth and semismooth technique, the local quadratic convergence of the proposed method under some assumptions is established.

##### 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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