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

被引：23

作者：

Liu, Xiao-Hong ^{[1
]}

Huang, Zheng-Hai ^{[1
]}

机构：

[1] Tianjin Univ, Sch Sci, Dept Math, Tianjin 300072, Peoples R China

来源：

MATHEMATICAL METHODS OF OPERATIONS RESEARCH | 2009年 / 70卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Linear programming; Symmetric cone; Euclidean Jordan algebra; Smoothing Newton algorithm; NONLINEAR COMPLEMENTARITY-PROBLEMS; JORDAN ALGEBRAS; CONVERGENCE;

D O I：

10.1007/s00186-008-0274-1

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：385 / 404

页数：20

共 41 条

[1] A smoothing Newton algorithm based on a one-parametric class of smoothing functions for linear programming over symmetric cones
Xiao-Hong Liu
Zheng-Hai Huang
Mathematical Methods of Operations Research, 2009, 70 : 385 - 404
[2] SMOOTHING NEWTON ALGORITHM BASED ON A REGULARIZED ONE-PARAMETRIC CLASS OF SMOOTHING FUNCTIONS FOR GENERALIZED COMPLEMENTARITY PROBLEMS OVER SYMMETRIC CONES
Liu, Xiao-Hong
Gu, Wei-Zhe
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2010, 6 (02) : 363 - 380
[3] Smoothing Newton algorithm for symmetric cone complementarity problems based on a one-parametric class of smoothing functions
Ni T.
Gu W.-Z.
Journal of Applied Mathematics and Computing, 2011, 35 (1-2) : 73 - 92
[4] Smoothing Newton Algorithm for Linear Programming over Symmetric Cones
刘晓红
倪铁
Transactions of Tianjin University, 2009, 15 (03) : 216 - 221
[5] Smoothing Newton Algorithm for Linear Programming over Symmetric Cones
刘晓红
倪铁
Transactions of Tianjin University, 2009, (03) : 216 - 221
[6] Smoothing Newton algorithm for linear programming over symmetric cones
Liu X.
Ni T.
Transactions of Tianjin University, 2009, 15 (03) : 216 - 221
[7] A smoothing Newton method based on a one-parametric class of smoothing function for SOCCP
Liu L.
Liu S.
Journal of Applied Mathematics and Computing, 2011, 36 (1-2) : 473 - 487
[8] A one-parametric class of smoothing functions and an improved regularization Newton method for the NCP
Tang, Jingyong
Zhou, Jinchuan
Fang, Liang
OPTIMIZATION, 2016, 65 (05) : 977 - 1001
[9] EXTENSION OF SMOOTHING NEWTON ALGORITHMS TO SOLVE LINEAR PROGRAMMING OVER SYMMETRIC CONES
Huang, Zhenghai
Liu, Xiaohong
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2011, 24 (01) : 195 - 206
[10] Extension of smoothing Newton algorithms to solve linear programming over symmetric cones
Zhenghai Huang
Xiaohong Liu
Journal of Systems Science and Complexity, 2011, 24 : 195 - 206

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