A REGULARIZED SMOOTHING NEWTON METHOD FOR SYMMETRIC CONE COMPLEMENTARITY PROBLEMS

被引：78
|
作者：
Kong, Lingchen [1 ]
Sun, Jie [2 ,3 ]
Xiu, Naihua [1 ]
机构：
[1] Beijing Jiaotong Univ, Dept Appl Math, Beijing 100044, Peoples R China
[2] Natl Univ Singapore, Dept Decis Sci, Singapore, Singapore
[3] Natl Univ Singapore, Singapore MIT Alliance, Singapore, Singapore
来源：
SIAM JOURNAL ON OPTIMIZATION | 2008年 / 19卷 / 03期
基金：
中国国家自然科学基金;
关键词：
symmetric cone complementarity problem; monotonicity; natural residual function; regularized smoothing method; quadratic convergence;
D O I：
10.1137/060676775
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper extends the regularized smoothing Newton method in vector complementarity problems to symmetric cone complementarity problems (SCCP), which includes the nonlinear complementarity problem, the second-order cone complementarity problem, and the semidefinite complementarity problem as special cases. In particular, we study strong semismoothness and Jacobian nonsingularity of the total natural residual function for SCCP. We also derive the uniform approximation property and the Jacobian consistency of the Chen-Mangasarian smoothing function of the natural residual. Based on these properties, global and quadratical convergence of the proposed algorithm is established.
引用
收藏
页码：1028 / 1047
页数：20
相关论文
共 50 条
  • [31] A new class of smoothing functions and a smoothing Newton method for complementarity problems
    Zhu, Jianguang
    Hao, Binbin
    [J]. OPTIMIZATION LETTERS, 2013, 7 (03) : 481 - 497
  • [32] Smoothing Functions and Smoothing Newton Method for Complementarity and Variational Inequality Problems
    L. Qi
    D. Sun
    [J]. Journal of Optimization Theory and Applications, 2002, 113 : 121 - 147
  • [33] Smoothing functions and smoothing Newton method for complementarity and variational inequality problems
    Qi, L
    Sun, D
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2002, 113 (01) : 121 - 147
  • [34] A globally convergent smoothing Newton method for the second order cone complementarity approach of elastoplasticity problems
    Jin, Yimin
    Li, Zhizhi
    Zhang, Huai
    Shi, Yaolin
    [J]. COMPUTERS AND GEOTECHNICS, 2023, 156
  • [35] Smoothing method for mathematical programs with symmetric cone complementarity constraints
    Yan, Tao
    Fukushima, Masao
    [J]. OPTIMIZATION, 2011, 60 (1-2) : 113 - 128
  • [36] A smoothing Newton method for the second-order cone complementarity problem
    Tang, Jingyong
    He, Guoping
    Dong, Li
    Fang, Liang
    Zhou, Jinchuan
    [J]. APPLICATIONS OF MATHEMATICS, 2013, 58 (02) : 223 - 247
  • [37] A smoothing Newton method for the second-order cone complementarity problem
    Jingyong Tang
    Guoping He
    Li Dong
    Liang Fang
    Jinchuan Zhou
    [J]. Applications of Mathematics, 2013, 58 : 223 - 247
  • [38] A new nonmonotone smoothing Newton method for the symmetric cone complementarity problem with the Cartesian P0-property
    Liu, Xiangjing
    Liu, Sanyang
    [J]. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2020, 92 (02) : 229 - 247
  • [39] Smoothing Newton method for generalized complementarity problems based on a new smoothing function
    Zheng, Xiuyun
    Shi, Jiarong
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 231 : 160 - 168
  • [40] A Smoothing Newton Method with Fischer-Burmeister Function for Second-Order Cone Complementarity Problems
    Narushima, Yasushi
    Sagara, Nobuko
    Ogasawara, Hideho
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2011, 149 (01) : 79 - 101
12345