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http://dx.doi.org/10.14317/jami.2011.29.5_6.1511

ANALYSIS OF SMOOTHING NEWTON-TYPE METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS  

Zheng, Xiuyun (Department of Applied Mathematics, Xidian University)
Publication Information
Journal of applied mathematics & informatics / v.29, no.5_6, 2011 , pp. 1511-1523 More about this Journal
Abstract
In this paper, we consider the smoothing Newton method for the nonlinear complementarity problems with $P_0$-function. The proposed algorithm is based on a new smoothing function and it needs only to solve one linear system of equations and perform one line search per iteration. Under the condition that the solution set is nonempty and bounded, the proposed algorithm is proved to be convergent globally. Furthermore, the local superlinearly(quadratic) convergence is established under suitable conditions. Preliminary numerical results show that the proposed algorithm is very promising.
Keywords
Nonlinear complementarity problem; Smoothing Newton method; $P_0$-function; Global and superlinear(quadratic) convergence;
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