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应用数学学报  2013, Vol. 36 Issue (3): 439-447    DOI:
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变动控制结构下几乎-锥-凸映射的标量函数刻画
余国林1, 刘三阳2
1. 北方民族大学信息与系统科学研究所, 银川 750021;
2. 西安电子科技大学理学院, 西安 710071
Scalar Characterizations of Nearly-cone-convex Mappings in Variable Domination Structures
YU Guolin1, LIU Sanyang2
1. Research Institute of Information and System Computation Science, Beifang University of Nationalities, Yinchuan 750021;
2. Department of Applied Mathematics, Xidian University, Xi'an 750021
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摘要 本文讨论变动控制结构下广义锥凸映射的线性和非线性标量函数的刻画问题.首先在变动序拓扑向量空间中证明了由正极锥的极方向所刻画的向量值映射的几乎-锥-凸性;其次,对变动控制结构引入了一种非线性标量函数,并利用这种非线性标量函数,得到了几乎-锥-凸向量值映射的标量刻画.
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余国林
刘三阳
关键词变动控制结构   非线性标量化   几乎-锥-凸性   极方向     
Abstract: This paper deals with the linear and nonliner scalarization of generalized cone-convex maps under the variable domination structures. Firstly, in the variable orderings topology vector spaces, it is shown that the nearly-cone-convexity of the vector-valued maps can be characterized by means of the extreme directions of the positive polar cone. Secondly, a nonlinear scalariztion funciton is introduced for a variable domination structure. This nonlinear function is then applied to characterize the nearly-cone-convex vector-valued mappings.
Key wordsvariable domination structure   nonlinear scalariztion   nearly-cone-convexity   extreme direction   
收稿日期: 2011-03-16;
基金资助:国家青年自然科学基金(10901004);教育部科学技术研究重点项目(212204);宁夏自然科学基金项目(NZ12207)以及宁夏高等学校科学技术研究重点项目(NGY2012092)资助项目.
引用本文:   
余国林,刘三阳. 变动控制结构下几乎-锥-凸映射的标量函数刻画[J]. 应用数学学报, 2013, 36(3): 439-447.
YU Guolin,LIU Sanyang. Scalar Characterizations of Nearly-cone-convex Mappings in Variable Domination Structures[J]. Acta Mathematicae Applicatae Sinica, 2013, 36(3): 439-447.
 
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