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Improved smoothing Newton methods for symmetric cone complementarity problems

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Abstract

There recently has been much interest in smoothing Newton method for solving nonlinear complementarity problems. We extend such method to symmetric cone complementarity problems (SCCP). In this paper, we first investigate a one-parametric class of smoothing functions in the context of symmetric cones, which contains the Fischer–Burmeister smoothing function and the CHKS smoothing function as special cases. Then we propose a smoothing Newton method for the SCCP based on the one-parametric class of smoothing functions. For the proposed method, besides the classical step length, we provide a new step length and the global convergence is obtained. Finally, preliminary numerical results are reported, which show the effectiveness of the two step lengthes in the algorithm and provide efficient domains of the parameter for the complementarity problems.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Yuan Min Li & Xing Tao Wang

  2. National Key Laboratory of Tunable Laser Technology, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    De Yun Wei

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  1. Yuan Min Li
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  2. Xing Tao Wang
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  3. De Yun Wei
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Correspondence to Yuan Min Li.

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Li, Y.M., Wang, X.T. & Wei, D.Y. Improved smoothing Newton methods for symmetric cone complementarity problems. Optim Lett 6, 471–487 (2012). https://doi.org/10.1007/s11590-010-0274-y

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  • DOI: https://doi.org/10.1007/s11590-010-0274-y

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