A Mizuno-Todd-Ye predictor-corrector infeasible-interior-point method for linear programming over symmetric cones

被引：6
|
作者：
Yang, Ximei [1 ]
Zhang, Yinkui [1 ]
Liu, Hongwei [2 ]
Pei, Yonggang [1 ]
机构：
[1] Henan Normal Univ, Sch Math & Informat Sci, Henan Engn Lab Big Data Stat Anal & Optimal Contr, Xinxiang 453007, Peoples R China
[2] Xidian Univ, Sch Math & Stat, Xian 710071, Peoples R China
来源：
NUMERICAL ALGORITHMS | 2016年 / 72卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Jordan algebra; Symmetric cones; Linear programming; Infeasible-interior-point methods; Iteration bound; POLYNOMIAL CONVERGENCE; JORDAN ALGEBRAS; ALGORITHMS; NEIGHBORHOOD;
D O I：
10.1007/s11075-015-0074-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We propose a Mizuno-Todd-Ye predictor-corrector infeasible-interior-point method for linear programming over symmetric cones by using a wide neighborhood. In the corrector step, we adopt a special strategy, which can ensure the existence of a step size to keep every iteration in the given small neighborhood. By using an elegant analysis, we obtain the iteration bounds for a commutative class of directions. In particular, the iteration bound is for the Nesterov-Todd search direction, and for the xs and sx search direction. To our knowledge, the obtained iteration bounds match the currently best known iteration bounds for infeasible-interior-point method. Some preliminary numerical results are provided as well.
引用
收藏
页码：915 / 936
页数：22
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