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A new smoothing and regularization Newton method for P 0-NCP

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Abstract

The nonlinear complementarity problem (denoted by NCP(F)) can be reformulated as the solution of a nonsmooth system of equations. In this paper, we propose a new smoothing and regularization Newton method for solving nonlinear complementarity problem with P 0-function (P 0-NCP). Without requiring strict complementarity assumption at the P 0-NCP solution, the proposed algorithm is proved to be convergent globally and superlinearly under suitable assumptions. Furthermore, the algorithm has local quadratic convergence under mild conditions. Numerical experiments indicate that the proposed method is quite effective. In addition, in this paper, the regularization parameter ε in our algorithm is viewed as an independent variable, hence, our algorithm seems to be simpler and more easily implemented compared to many previous methods.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, China

    Changfeng Ma

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  1. Changfeng Ma
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Correspondence to Changfeng Ma.

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The project supported by Fujian Natural Science Foundation  (Grant No. 2009J01002) and National Natural Science Foundation of China (Grant No. 10661005).

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Ma, C. A new smoothing and regularization Newton method for P 0-NCP. J Glob Optim 48, 241–261 (2010). https://doi.org/10.1007/s10898-009-9489-9

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