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A new nonmonotone smoothing Newton method for the symmetric cone complementarity problem with the Cartesian \(P_0\)-property

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Abstract

We present a new smoothing Newton method for the symmetric cone complementarity problem with the Cartesian \(P_0\)-property. The new method is based on a new smoothing function and a nonmonotone line search which contains a monotone line search as a special case. It is proved that the new method is globally and locally superlinearly/quadratically convergent under mild conditions. Preliminary numerical results are also reported which indicate the proposed method is promising.

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Acknowledgements

We thank editors and two anonymous reviewers for their careful work and thoughtful suggestions that have greatly improved our article. The authors’ work is supported by National Natural Science Foundation of China (Grant No. 61877046).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, China

    Xiangjing Liu & Sanyang Liu

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  1. Xiangjing Liu
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  2. Sanyang Liu
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Correspondence to Xiangjing Liu.

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Liu, X., Liu, S. A new nonmonotone smoothing Newton method for the symmetric cone complementarity problem with the Cartesian \(P_0\)-property. Math Meth Oper Res 92, 229–247 (2020). https://doi.org/10.1007/s00186-020-00709-7

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  • DOI: https://doi.org/10.1007/s00186-020-00709-7

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