Tucker定理在线性锥系统的推广  

Tucker Theorem generalized to 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：《华中师范大学学报（自然科学版）》2008年第3期339-342,共4页Journal of Central China Normal University：Natural Sciences

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,本文应用对偶锥的概念和线性锥系统的Farkas引理,给出了一般线性锥系统的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,且线性系统和一般线性锥系统的表达形式相同.这为进一步研究锥规划提供了便利.For generalizing Tucker Theorem that is one of the basic theories of linear programming to the conic linear system, the paper applies the dual cone and Farksa Lemma of the conic linear system, and proves Tucker Theorem of the conic linear system. The conlusion shows that, to any conic linear system including homogeneous linear inequalities and its dual system, Tucker Theorem exists, and the expressions of Tucher Theorem are the same both in the linear system and in the conic linear system. It offers the convenience for further studying 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]