By using the vector variational inequality related to radial epiderivative,we give a number of necessary and sufficient conditions for Henig efficiency,super efficiency and cone-super efficiency of set-valued optimization under the framework of locally convex topological vector spaces,which generalizes some known related results.
利用与仿射上导数相关的向量变分不等式的真有效性,对局部凸拓扑向量空间中的集值优化问题的Henig有效性、超有效性、锥超有效性等给出了一些充分、必要条件,从而推广了一些已知的相关结论。
In the framework of locally convex topological vector spaces, we introduce the concepts of radial epiderivative and contingent epiderivative, and discuss the relationship between them.
本文在局部凸拓扑向量空间的框架下，介绍了仿射上导数、伴随上导数的概念，指出了两者的联系；提出了与仿射上导数相关的向量变分不等式问题(VVIP)_R，并给出了它的各种有效解对、真有效解对的定义；利用它们对无约束的集值映射向量优化问题的各种有效对、真有效对，分别给出了一系列充分、必要条件；此外还仿照[17]中f-伴随导数的概念，对集值映射提出了一种新的导数概念：f-仿射导数，利用它对集值映射向量优化问题的f-有效对给出了一个充分必要条件。
In this paper, the necessary and sufficient conditions of Geoffrion efficient solutions in vector set-valued optimization problem with vector variational inequality are obtained by using the concept of contingent epiderivative, which has been introduced by Jahn and Rauh.
利用Jahn与Rauh提出的集值映射的切上导数概念,解决了以向量变分不等式的形式给出向量集值优化问题的Geoffrion有效解的充分必要条件。
In this paper, the necessary and sufficient conditions of various proper efficient solutions in vector set-valued optimization problem are obtained by using the concept of contingent epiderivative,which has been introduced by Jahn and Rauh.
利用Jahn与Rauh提出的集值映射的切上导数概念 ,给出了向量集值映射最优化问题的各种有效解的充分与必要条
By using the concept of contingent epiderivative,radial contingent epiderivative,it presents the necessary and sufficient conditions for weakly efficient solution,globally efficient solution,Henig efficient solution and C-superefficient solution to the vector equilibrium problems.
利用映射的切上导数,径向切上导数给出了向量均衡问题弱有效解,整体有效解,Hen ig有效解以及C-超有效解的充分必要条件。
The concept of the generalized gradient in sense of strong efficiency is introduced by epiderivative for a set-valued map in ordered Banach spaces.
在锥序Banach空间中利用集值映射的上图导数引进了强有效意义下的广义梯度,在下C-半连续条件下,利用凸集分离定理证明了该广义梯度的存在性,由此建立了集值向量优化问题强有效解在广义梯度下的最优性条件。
ordinary upper derivative of a set function
集函数的寻常上导数
"In calculus, the derivative equals zero or does not exist at a function's minimum point."
在微积分中,在函数的极小值点上导数等于零或者不存在导数。
The Strictly Efficient Points of Set-valued Optimization Depicted with Contingent Derivatives;
用切上导数刻画集值优化的严有效点
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Derivable and Anti-derivable Linear Mappings on Von Neumann Algebra;
Von Neumann代数上的可导和反可导线性映射
The Derivations From the Lie Algebra of Skew Derivations on Quantum Torus to Its Modules
量子环面上的斜导子李代数模的导子
Generalized Jordan Derivation on Normed complex*-algebra;
复范数~*-代数上的广义Jordan导子
Inner Derivation Algebras of 5-Dimensional 3-Lie Algebras over Z_2
Z_2上5维3-Lie代数的内导子Lie代数
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Application of Derivative of Variable Upper Limit Integral in Physics
变上限积分求导数法在物理学中应用
Additivity of Jordan Maps and Biderivations on Nest Subalgebras;
套子代数上Jordan映射的可加性及双导子
The Derivation Problem of Piecewise Continuous Function at Piecewise Point;
分段连续函数在分段点上的求导问题
The Design and Realization of Advanced Mathematics Assist System Based on Network;
高等数学网上辅导系统的设计与实现
Stability of Bi-Jordan Derivations on Banach Algebra
Banach代数上双Jordan导子的稳定性
Generalized Lie Derivable Mappings at The Piont Zero on Nest Algebras
套代数上的零点广义Lie可导映射
Bi-Jordan Derivations on Jordan Algebras of Selfadjoint Operators
自伴算子的Jordan代数上的双Jordan导子
Generalized Jordan Derivations of Triangular Algebras
三角代数上的广义Jordan导子
Derivations of J-von Neumann Algebras in Π_1
Π_1空间上J-yon Neumann代数的导子
