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A family of new smoothing functions and a nonmonotone smoothing Newton method for the nonlinear complementarity problems

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Abstract

In this paper, based on a p-norm with p being any fixed real number in the interval (1,+∞), we introduce a family of new smoothing functions, which include the smoothing symmetric perturbed Fischer function as a special case. We also show that the functions have several favorable properties. Based on the new smoothing functions, we propose a nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems. The proposed algorithm only need to solve one linear system of equations. We show that the proposed algorithm is globally and locally superlinearly convergent under suitable assumptions. Numerical experiments indicate that the method associated with a smaller p, for example p=1.1, usually has better numerical performance than the smoothing symmetric perturbed Fischer function, which exactly corresponds to p=2.

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Authors and Affiliations

  1. Department of Mathematics, Xidian University, Xi’an, China, 710071

    Jianguang Zhu, Hongwei Liu & Changhe Liu

  2. Department of Mathematics, Henan University of Science and Technology, Luoyang, China

    Changhe Liu

Authors
  1. Jianguang Zhu
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  2. Hongwei Liu
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  3. Changhe Liu
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Corresponding author

Correspondence to Jianguang Zhu.

Additional information

This work is supported by the National Natural Science Foundation of China (Grant No. 61072144) and the Fundamental Research Funds for the Central Universities (Grant No. JY10000970004).

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Zhu, J., Liu, H. & Liu, C. A family of new smoothing functions and a nonmonotone smoothing Newton method for the nonlinear complementarity problems. J. Appl. Math. Comput. 37, 647–662 (2011). https://doi.org/10.1007/s12190-010-0457-9

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  • DOI: https://doi.org/10.1007/s12190-010-0457-9

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