对偶定理

较多有效解类的最优性条件和Lagrange对偶定理

The optimality conditions and the Lagrange duality theorems for several kinds of major efficient solutions

用环论的方法证明了群分次环上的双积对偶定理，主要结果是当G为有限群时，R＃kG＃。

In this paper , using some techniques from ring theory , duality theorems for group-graded rings in double products are proved . The main result is that when G is finite , R # kG # .

（F，ρ）s-凸多目标规划的逆对偶定理

Converse Dual Theorem of ( F ,ρ) _s-Convex Multiobjective Programming

DC规划的一个对偶定理

A Duality Theorem for DC Programming

非光滑Fuzzy多目标规划的Fuzzy有效解的Mond-weir型对偶定理

Mond-Weir type Duality for Fuzzy Efficient Solutions in Nonsmooth Fuzzy Multiobjective Programming

区域上Hardy空间的对偶定理

The dual theorem of Hardy space on domains in r ~ n

无约束向量极值问题的Lagrange对偶定理

Lagrange Dual Theorem for Unconstrained Vector Optimization Problems

在（F，ρ）s-凸函数的基础上，给出了多目标规划的两个逆对偶定理。

On the basis of ( F ,ρ) _s Convex functions two converse dual theorems of multiobjective programming are given under .

广义Hamming重量上、下界的对偶定理

A Dual Theorem of Upper and Lower Bounds on the Generalized Hamming Weights

广义凸多目标规划的Wolfe型对偶定理

The Wolfe Type Duality in the Generalized Convex Multiobjective Programming

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。

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 .

依所给约束函数的不同条件来恰当划分约束集，在广义（F，ρ）凸性下，证明了弱对偶定理、强对偶定理以及严格逆对偶定理。

Under the different conditions of the constrained functions , dividing constrained sets properly , and under generalized ( F , ρ) convexity , the theorems of the weak duality , strong duality and strictly reverse duality are testified .

本文将射影平面上二次曲线的Steiner定理〔1〕及其逆定理、对偶定理推广到n维射影空间Pn的二次超曲面上。

In this paper , the Steiner theorem . and its contra-theorem , duality-theorem of conical section on projective plane are generalized to the quadric-hypersurface of n-dimensional projective space .

本文在广义（F，ρ）&凸性条件下，利用有效解概念，给出了多目标分式规划的某些对偶定理。

For a multiobjective fractional program which involves inequality and equality constraints , this paper derives some duality theorems from using the concept of efficiency coupled with some generalized ( F ,ρ) - convexity assumptions on the objective and constraint functions .

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。

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 .

一类多目标优化控制问题的两个弱对偶定理

Two weak duality theorems for a class of multiobjective optimal control problems

集合函数多目标规划的拉格朗日型对偶定理

Lagrange Duality Theorem for Multiobjective Programming with Set Functions

关于U.Neri的对偶定理的一点注记

A note on a paper of U. neri 's

线性拓扑空间中一般向量极值问题的ε-共轭对偶定理

ε - Conjugate Duality Theorem of Vector Extremum Problems in Linear Topological Spaces

G-旋模型场代数中的对偶定理

The Duality Theorem in Field Algebra of G-Spin Model

半序局部凸空间的对偶定理

The Dual Theorems of Partially Ordered Locally Convex Spaces

多目标最优化在实际生产领域有着广泛的应用，最优性条件和对偶定理是人们研究的主要内容。

Multiobjective optimization is applied in extensive areas .

检错码的对偶定理

A Dual Theorem on Error Detection Codes

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

The notes for the structure of linear time & varying system and the duality theorem

S&可分解算子的谱对偶定理

A Duality Theorem for S-Residually Decomposable Operators

对偶定理的一个推广

A generalization of the duality theorems

多值模代数方程组的对偶定理

Duality Principle of Multiple-Valued Modulo-Algebra Equations

密勒定理、密勒对偶定理及应用

The Original Miller 's Theorem , its Dual Version of the Miller 's Theorem and their Applications

然后给出定理2.3的一个正确的证明.同时指出文献[1]中的对偶定理3.4是不正确的。

Meanwhile , we also point out that Theorem 3.4 of [ 1 ] is not true .

本文讨论了一类多目标广义凸分式规划的对偶定理，其结果是对张吉军的对偶定理的推广。

The paper discusses the duality theorems for the generalized convex multiobjective fractional programming and get a more general result .