A Homogeneous Smoothing-type Algorithm for Symmetric Cone Linear Programs

被引：0

作者：

Gu, Wei-zhe ^{[1
]}

Huang, Zheng-Hai ^{[1
]}

机构：

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

来源：

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2014年 / 30卷 / 03期

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

linear program; symmetric cone; Euclidean Jordan algebra; smoothing algorithm; global convergence; INTERIOR-POINT ALGORITHMS; ONE-PARAMETRIC CLASS; COMPLEMENTARITY-PROBLEMS; JORDAN ALGEBRAS; CONVERGENCE; EXTENSION;

D O I：

10.1007/s10255-014-0409-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate a smoothing-type algorithm for solving the symmetric cone linear program ((SCLP) for short) by making use of an augmented system of its optimality conditions. The algorithm only needs to solve one system of linear equations and to perform one line search at each iteration. It is proved that the algorithm is globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, the algorithm may correctly detect solvability of (SCLP). Furthermore, if (SCLP) has a solution, then the algorithm will generate a solution of (SCLP), and if the problem is strongly infeasible, the algorithm will correctly detect infeasibility of (SCLP).

引用

页码：647 / 662

页数：16