Generic well posedness in linear programming

被引：0
|
作者：
Lucchetti, Roberto [1 ]
Radrizzani, Paola [1 ]
Villa, Silvia [2 ]
机构：
[1] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy
[2] Univ Genoa, Dipartimento Matemat, I-16146 Genoa, Italy
来源：
PACIFIC JOURNAL OF OPTIMIZATION | 2008年 / 4卷 / 03期
关键词：
well posedness; linear programming; genericity;
D O I：
暂无
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：
We consider the following pair of linear programming problems in duality: [GRAPHICS] parameterized by the m x n matrix A defining the inequality constraints. The main result of the paper states that in the case m >= n the set S of well posed problems in a very strong sense is a generic subset of the set of problems having solution. Generic here means that, S is an open and dense set whose complement is contained in a finite union of algebraic surfaces of dimension less than mn.
引用
收藏
页码：513 / 525
页数：13
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