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

Author

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  • Nan Lu

    (Xidian University)

  • Zheng-Hai Huang

    (Tianjin University
    Tianjin University)

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.

Suggested Citation

  • Nan Lu & Zheng-Hai Huang, 2014. "A Smoothing Newton Algorithm for a Class of Non-monotonic Symmetric Cone Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 446-464, May.
  • Handle: RePEc:spr:joptap:v:161:y:2014:i:2:d:10.1007_s10957-013-0436-z
    DOI: 10.1007/s10957-013-0436-z
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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. Yong-Jin Liu & Li-Wei Zhang & Yin-He Wang, 2006. "Some Properties Of A Class Of Merit Functions For Symmetric Cone Complementarity Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 23(04), pages 473-495.
    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.
    5. Xiao-Hong Liu & Zheng-Hai Huang, 2009. "A smoothing Newton algorithm based on a one-parametric class of smoothing functions for linear programming over symmetric cones," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 385-404, October.
    6. Sangho Kum & Yongdo Lim, 2010. "Penalized complementarity functions on symmetric cones," Journal of Global Optimization, Springer, vol. 46(3), pages 475-485, March.
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    Cited by:

    1. Jingyong Tang & Hongchao Zhang, 2021. "A Nonmonotone Smoothing Newton Algorithm for Weighted Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 679-715, June.
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