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关于凸分析中代数闭包和向量闭包的概念研究

On the Concepts of the Algebraic Closure and the Vector Closure in Convex Analysis
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摘要 研究了线性空间中代数闭包和向量闭包的关系,给出了凸集的代数闭包是凸集的新证明,利用代数闭包与向量闭包的关系,得到了一个涉及向量闭包的分离定理。 Firstly, the relation between the algebraic closure and the vector closure is studied. Sec ondly, a new proof that the algebraic closure of the convex set is convex is given. Finally, by the relation between the algebraic closure and the vector closure, a separation theorem involving the vector closure is obtained
作者 周志昂
出处 《重庆理工大学学报(自然科学)》 CAS 2013年第1期116-118,共3页 Journal of Chongqing University of Technology:Natural Science
基金 重庆理工大学高等数学课程建设和团队建设专项经费资助项目(0101129001)
关键词 代数闭包 向量闭包 分离定理 algebraic closure vector closure separation theorem
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参考文献4

  • 1Jahn J. Vector Optimization-Theory,Applications and Extensions[M].Second Edition.Berlin:Springer,2011.
  • 2史树中.凸分析[M]上海:上海科学技术出版社,1990.
  • 3Adán M,Novo V. Weak efficiency in vector optimization using a closure of algebraic type under cone-convexlikeness[J].European Journal of Operational Research,2003.641-653.
  • 4Tiel J V. Convex Analysis-An Introductory Text[M].New York:John Wiley and Sones,1984.

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