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A smoothing Newton algorithm based on a one-parametric class of smoothing functions for linear programming over symmetric cones

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  • Xiao-Hong Liu
  • Zheng-Hai Huang

Abstract

In this paper, we introduce a one-parametric class of smoothing functions which contains the Fischer–Burmeister smoothing function and the CHKS smoothing function as special cases. Based on this class of smoothing functions, a smoothing Newton algorithm is extended to solve linear programming over symmetric cones. The global and local quadratic convergence results of the algorithm are established under suitable assumptions. The theory of Euclidean Jordan algebras is a basic tool in our analysis. Copyright Springer-Verlag 2009

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:70:y:2009:i:2:p:385-404
    DOI: 10.1007/s00186-008-0274-1
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    References listed on IDEAS

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    1. S. H. Schmieta & F. Alizadeh, 2001. "Associative and Jordan Algebras, and Polynomial Time Interior-Point Algorithms for Symmetric Cones," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 543-564, August.
    2. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
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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.
    2. 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.
    3. 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.
    4. Jingyong Tang & Jinchuan Zhou, 2020. "Smoothing inexact Newton method based on a new derivative-free nonmonotone line search for the NCP over circular cones," Annals of Operations Research, Springer, vol. 295(2), pages 787-808, December.

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