Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ANALYSIS OF SMOOTHING NEWTON-TYPE METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS

  • Zheng, Xiuyun (Department of Applied Mathematics, Xidian University)
  • Received : 2010.09.12
  • Accepted : 2010.12.09
  • Published : 2011.09.30
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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.

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References

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