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A Smoothing Newton Algorithm for a Class of Non-monotonic Symmetric Cone Linear Complementarity Problems

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Abstract

Recently, the study of symmetric cone complementarity problems has been a hot topic in the literature. Many numerical methods have been proposed for solving such a class of problems. Among them, the problems concerned are generally monotonic. In this paper, we consider symmetric cone linear complementarity problems with a class of non-monotonic transformations. A smoothing Newton algorithm is extended to solve this class of non-monotonic symmetric cone linear complementarity problems; and the algorithm is proved to be well-defined. In particular, we show that the algorithm is globally and locally quadratically convergent under mild assumptions. The preliminary numerical results are also reported.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 11171252 and 11301409).

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Authors and Affiliations

  1. Department of Mathematics, Xidian University, Xi’An, 710071, P.R. China

    Nan Lu

  2. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, P.R. China

    Zheng-Hai Huang

  3. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, P.R. China

    Zheng-Hai Huang

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  1. Nan Lu
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  2. Zheng-Hai Huang
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Correspondence to Zheng-Hai Huang.

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Communicated by Liqun Qi.

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Lu, N., Huang, ZH. A Smoothing Newton Algorithm for a Class of Non-monotonic Symmetric Cone Linear Complementarity Problems. J Optim Theory Appl 161, 446–464 (2014). https://doi.org/10.1007/s10957-013-0436-z

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  • DOI: https://doi.org/10.1007/s10957-013-0436-z

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