线性锥系统的Tucker型相容性定理  

Tucker Consistency Theorem of the Conic Linear System

作　　者：安中华[1] 安琼[2] 安琪[3] 

机构地区：[1]湖北第二师范学院数学与计量经济系,武汉430205 [2]中国科学院南京土壤研究所,南京210008 [3]华中科技大学数学系,武汉430074

出　　处：《大学数学》2009年第4期28-31,共4页College Mathematics

基　　金：国家重点基础研究发展规划项目(2002CB410805)

摘　　要：为了将线性规划中的基础理论之一的Tucker定理推广到一般线性锥系统上,应用对偶锥的概念和线性锥系统的Farkas引理,给出了一般线性系统的Tucker定理,所得结果显示含齐次线性不等式组的线性锥系统和它的对偶系统都存在Tucker定理,且Tucker定理结论的表达式基本相同,这为进一步研究锥规划提供了便利.Tucker Theorem is one of the basic theories of linear programming. For generalizing Tucker Theorem to the conic linear system, the authors applies the dual cone and Farkas Lemma of the conic linear system, and proves Tucker Theorem of the conic linear system. The conclusion shows that Tucker Theorem exists in any conic linear system including homogeneous linear inequalities and its dual system. Furthermore, the expressions of Tucker Theorem conclusion are same. So it was helpful to the next studying of the conic programming.

关 键 词：线性锥系统 对偶锥 FARKAS引理 Tucker定理 

分 类 号：O177.2[理学—数学]