duality theorem
英 [djuːˈæləti ˈθɪərəm]
美 [duːˈæləti ˈθiːərəm]
对偶定理
双语例句
- The duality theory is the basic theory for mathematical planning in which the study of weak duality theorem under different controlling conditions is an important part of duality theorem research.
对偶理论是数学规划的理论基础，其中在各种约束条件下对弱对偶定理的研究是对偶理论研究的重要组成部分。 - Lagrange Duality Theorem for Multiobjective Programming with Set Functions
集合函数多目标规划的拉格朗日型对偶定理 - Finally, the generalized dual model of the problem ( VP) is presented with the help of upper subdifferential of function, and a weak duality theorem is given.
接着，利用函数的上次微分构造了不可微向量优化问题（VP）的广义对偶模型，并且在适当的弱凸性条件下建立了弱对偶定理。 - The H α conjugate duality programming for general multiobjective programming and its weak duality theorem were proposed. Then the strong duality theorem under some conditions was proved using H α subdifferential.
然后对一般类型的多目标规划问题，定义了Hα-共轭对偶问题，证明了弱对偶定理，并利用Hα-次可微性证明了在一定条件下的强对偶定理。 - The notes for the structure of linear time& varying system and the duality theorem
关于线性时变系统的结构和对偶定理的注记美国人的时间观 - ε-Conjugate Duality Theorem of Vector Extremum Problems in Linear Topological Spaces
线性拓扑空间中一般向量极值问题的ε-共轭对偶定理 - A Duality Theorem for S-Residually Decomposable Operators
S&可分解算子的谱对偶定理 - The Duality Theorem in Field Algebra of G-Spin Model
G-旋模型场代数中的对偶定理 - Abstract In this paper, several concepts such as pseudoconvex, strictly pseudoconvex and quasiconvex for nonsmooth functions are presented by directional derivatives. A dual problem is introduced and duality theorems such as weak duality theorem, strong duality theorem, strickly converse duality theorem are proved.
利用方向导数对非光滑函数引入了伪凸、严格伪凸和拟凸等概念，给出了非光滑多目标分式规划的对偶问题，并证明了弱对偶定理、强对偶定理及严格对偶定理。 - In this paper, tbe authors proved the principle of duality of projective geometry and the dual theorem of curve of second degree.
采用代数方法证明了射影几何的时偶原则及二次曲线的对偶定理。 - In this chapter, the property of the solution of the prime problem and the duality theorem of the mode of multi-class support vector machines are presented. Also the strict proof of these theories are given.
本文在二类支持向量机对偶理论的基础上，针对多分类支持向量机的数学模型，给出原始问题解的性质定理以及原始问题和对偶问题解的关系定理，并进行了严格的理论证明。 - Zhu had deduced generalized Fenchel's duality theorem in [ 8], and further applied it to Minimum Discrimination Information ( MDI) problem.
朱德通在文[8]中导出广义的Fenchel对偶定理，并将此定理成功地应用于带约束的最小区别信息量问题（简称MDI问题）。 - The properties of rough subalgebra are studied. The major result of getting involves substitution, necessary and sufficient condition of the rough subalgebra, homomorphism and duality theorem.
讨论了粗糙子代数的性质，得到主要结果：置换性、粗糙子代数的充要条件、同态映射、二重性定理等。 - In this paper, the duality theorems of arranging sequence theorem and Chebyshev inequality are given, and arranging sequence theorem, Chebyshev inequality and their duality theorems are generalized.
给出了排序定理和Chebyshev不等式的对偶定理，并对排序定理、Chebyshev不等式及其对偶定理进行了推广。 - At the same time, vector-valued Lagrange duality of vector extremum problems are established, including weak duality, strong duality and converse duality theorem in linear space.
同时，建立了向量极值问题的向量值Lagrange对偶，其中包括弱对偶定理，强对偶定理，逆对偶定理。 - Lagrange Duality and Alternative Theorem of Vector Optimization Problem
向量最优化问题的Lagrange对偶与择一定理 - Some properities of ( F,ρ)-invariant convexity functions are given, the weak duality theorem and the direct duality theorem of multiobjective programming for ( F,ρ)-invariant convexity functions are presented.
给出了（F，ρ）-不变凸函数的一些性质，提出了（F，ρ）-不变凸函数多目标规划的弱对偶定理和直接对偶定理。 - The Duality of Upper Bound Theorem and Lower Bound Theorem on Limit Theory and Programming Problem
极限上下限定律的对偶性和规划问题 - A Duality Theorem for DC Programming
DC规划的一个对偶定理 - Lagrange Duality and Saddle Points Theorem for Multiobjective Semidefinite Programming
多目标半定规划的Lagrange对偶与鞍点定理 - At the same time, duality problems are established also and both weak duality theorem and strong duality theorem are derived.
同时，研究了该问题的对偶问题，给出了相应的弱对偶定理和强对偶定理。 - Weak duality theorem is established under generalized convexity conditions.
在广义凸性条件下，建立了弱对偶性定理。 - This paper presented a duality theorem of infinite group grading ring which has a general structure and also give an example to show that this structure is untrivial.
本文得出了无限群分次环的一般结构下的对偶定理，另给出例子说明其非凡性。 - Duality theorem and saddle point optimality condition for the multiobjective semidefinite programming are then established.
然后利用鞍点的等价定义，得到多目标半定规划的鞍点最优性条件。 - This paper is concerned with Mond-Weir type duality about the joint efficient solution in group multiobjective programming, which contains the unsymmetrical objective functions and constraints. The weak duality theorem, the direct duality theorem and the inverse duality theorem are derived.
对于目标和约束均为不对称的群体多目标规划问题，本文研究它的联合有效解类的Mond&Weir型对偶性，得到了相应的弱对偶定理、直接对偶定理和逆对偶定理。