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
  • [1] A smoothing Newton method for symmetric cone complementarity problems
    Jia Tang
    Changfeng Ma
    [J]. Optimization Letters, 2015, 9 : 225 - 244
  • [2] A smoothing Newton method for symmetric cone complementarity problems
    Tang, Jia
    Ma, Changfeng
    [J]. OPTIMIZATION LETTERS, 2015, 9 (02) : 225 - 244
  • [3] A regularized smoothing Newton method for solving the symmetric cone complementarity problem
    Ma, Changfeng
    [J]. MATHEMATICAL AND COMPUTER MODELLING, 2011, 54 (9-10) : 2515 - 2527
  • [4] A New Smoothing Newton Method for Symmetric Cone Complementarity Problems
    Liu, Lixia
    Liu, Sanyang
    [J]. ALGORITHMIC ASPECTS IN INFORMATION AND MANAGEMENT, 2010, 6124 : 199 - 208
  • [5] A smoothing Newton method for symmetric cone complementarity problem
    Liu L.
    Liu S.
    Wu Y.
    [J]. J. Appl. Math. Comp., 1-2 (175-191): : 175 - 191
  • [6] A predictor-corrector smoothing Newton method for symmetric cone complementarity problems
    Liu, Lixia
    Liu, Sanyang
    Liu, Hongwei
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (07) : 2989 - 2999
  • [7] Improved smoothing Newton methods for symmetric cone complementarity problems
    Li, Yuan Min
    Wang, Xing Tao
    Wei, De Yun
    [J]. OPTIMIZATION LETTERS, 2012, 6 (03) : 471 - 487
  • [8] Improved smoothing Newton methods for symmetric cone complementarity problems
    Yuan Min Li
    Xing Tao Wang
    De Yun Wei
    [J]. Optimization Letters, 2012, 6 : 471 - 487
  • [9] A generalized smoothing Newton method for the symmetric cone complementarity problem
    Li, Yuan-Min
    Wei, Deyun
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2015, 264 : 335 - 345
  • [10] Sub-quadratic convergence of a smoothing Newton method for symmetric cone complementarity problems
    He, Yanling
    Lau, Chunyan
    [J]. 2015 27TH CHINESE CONTROL AND DECISION CONFERENCE (CCDC), 2015, : 3082 - 3087
12345