向量优化中free-disposal集的代数性质  

On Algebraic Properties of Free-Disposal Sets in Vector Optimization

作　　者：张万里[1] 刘金杰[1] 赵克全[1] 

机构地区：[1]重庆师范大学数学学院,重庆401331

出　　处：《西南师范大学学报（自然科学版）》2015年第3期32-36,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11301574;11271391);重庆市自然科学基金项目(CSTC2012jjA00002);重庆市研究生科研创新项目(CYS14136)

摘　　要：基于集合代数闭包和代数内部的概念,在free-disposal集条件下证明了代数闭包必是代数闭集,代数内部必是代数开集;研究了凸锥和与其对应的free-disposal集的代数性质,同时获得了两个free-disposal集和的代数性质;建立了两个free-disposal集的等价条件.Free-disposal sets is one of the important tools with which to study the characterizations of uni-fied solution in vector optimization .In this paper ,by applying the concepts of algebraic closure and interior of sets ,it has been proved that the algebraic closure is closed and the algebraic interior is open with the condition of the free-disposal set .T he properties of a convex cone and its corresponding free-disposal set are studied .The properties of the sum of two free-disposal sets have been obtained ,and the equivalent conditions between two free-disposal sets have been established .This paper extends some of the relevant results about free-disposal sets in recent literature .

关 键 词：向量优化 free-disposal集 代数性质 

分 类 号：O221.6[理学—运筹学与控制论]