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

被引：40

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 [运筹学与控制论]; 120117 [社会管理工程];

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 34 条

[1]

Alizadeh Farid., 2000, HDB SEMIDEFINITE PRO, P195

[2]

A NON-INTERIOR-POINT CONTINUATION METHOD FOR LINEAR COMPLEMENTARITY-PROBLEMS [J].