• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.653-668
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• 2011

This paper presents a new hybrid method for solving nonlinear complementarity problems with $P_0$-functions. It can be regarded as a combination of smoothing trust region method with ODE-based method and line search technique. A feature of the proposed method is that at each iteration, a linear system is only solved once to obtain a trial step, thus avoiding solving a trust region subproblem. Another is that when a trial step is not accepted, the method does not resolve the linear system but generates an iterative point whose step-length is defined by a line search. Under some conditions, the method is proven to be globally and superlinearly convergent. Preliminary numerical results indicate that the proposed method is promising.