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A new nonmonotone smoothing Newton method for the symmetric cone complementarity problem with the Cartesian $$P_0$$ P 0 -property

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  • Xiangjing Liu

    (Xidian University)

  • Sanyang Liu

    (Xidian University)

Abstract

We present a new smoothing Newton method for the symmetric cone complementarity problem with the Cartesian $$P_0$$ 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.

Suggested Citation

  • Xiangjing Liu & Sanyang Liu, 2020. "A new nonmonotone smoothing Newton method for the symmetric cone complementarity problem with the Cartesian $$P_0$$ P 0 -property," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(2), pages 229-247, October.
    • Handle: RePEc:spr:mathme:v:92:y:2020:i:2:d:10.1007_s00186-020-00709-7
    DOI: 10.1007/s00186-020-00709-7
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    References listed on IDEAS

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    1. Zheng-Hai Huang & Tie Ni, 2010. "Smoothing algorithms for complementarity problems over symmetric cones," Computational Optimization and Applications, Springer, vol. 45(3), pages 557-579, April.
    2. Lingchen Kong & Levent Tunçel & Naihua Xiu, 2009. "Vector-Valued Implicit Lagrangian For Symmetric Cone Complementarity Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(02), pages 199-233.
    3. Li, Yuan-Min & Wei, Deyun, 2015. "A generalized smoothing Newton method for the symmetric cone complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 335-345.
    4. Defeng Sun & Jie Sun, 2008. "Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 421-445, May.
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    Cited by:

    1. Jingyong Tang & Jinchuan Zhou & Hongchao Zhang, 2023. "An Accelerated Smoothing Newton Method with Cubic Convergence for Weighted Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 641-665, February.

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