Probabilistic analysis of condition numbers for linear programming

被引：14
|
作者：
Cheung, D [1 ]
Cucker, F [1 ]
机构：
[1] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China
来源：
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2002年 / 114卷 / 01期
关键词：
linear programming; condition numbers; probabilistic analysis of algorithms;
D O I：
10.1023/A:1015460004163
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 provide bounds for the expected value of the log of the condition number C(A) of a linear feasibility problem given by a n x m matrix A (Ref. 1). We show that this expected value is O(min{n, m log n}) if n > m and is \cat O(log n) otherwise. A similar bound applies for the log of the condition number C-R(A) introduced by Renegar (Ref. 2).
引用
收藏
页码：55 / 67
页数：13
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