对偶定理

词组短语

dual theorem · duality theorem

与对偶定理相关的网络例句 [注：此内容来源于网络，仅供参考]

A differential equation is introduced to construct canonical dual function. The corresponding perfect duality theory is established to show the relationship between the KKT points of the primal problem and the canonical dual problem.

通过引入常微分方程和构造Canonical对偶函数的局部形式，引入了相应的对偶定理，勾勒出了原问题的KKT点和对偶问题的KKT点两者之间的关系。

By Lagrange dual and scalarization of vector optimization, characterizations of solutions for which objective mapping satisfies weak convexity conditions are shown. The strongly and weak dual theorems for generalized subconvex-like mapping are obtained.

通过适当定义对偶问题和向量优化问题的标量化研究各解之间的关系，刻画目标映射满足弱凸性条件的优化问题解的特征，在目标映射是广义锥次类凸的条件下给出有关的对偶定理。

Upward dual pairs, dual theorem, positive extension, L-topology, semi-bounded, ordered locally convex spaces.

上偶对，对偶定理，正延拓，L-拓扑，半有界，半序局部凸空间，局部体空间

Based on much knowledge, contrasting to linear programming; we extend duality theorem (including weak duality theorem and strong duality theorem), complementary slack theorem to conic optimization. Hence we find out some significative conclusions and existing conditions under which their duality gap is zero of two optimizations.

在此基础上，通过与线性规划作对比，将对偶定理、互补松弛定理等推广到锥规划问题中，得到了一些有意义的结论，并且得到了这两个规划的零对偶间隙的存在条件。

This thesis is mainly to discuss the application of Desargues theorems and dual theorems in the elementary geometry.

中文摘要：本文主要研究Desargues定理及对偶定理在初等几何中的应用。

What I want to do is making it used in the elementary geometry, to prove the point of intersection in the same line and lines intersect at the same point .

由于Desargues定理及对偶定理是建立在仿射平面上的，而本文要讨论的是如何将其运用到以欧氏平面为基础的初等几何中，证明点共线和线共点的问题。

It is started with the Desargues theorems and dual theorems' formulation and proof of the elementary geometry, guaranteed the scientific of the method on the theoretical plane .

本文从Desargues定理及对偶定理的初等几何表述及证明入手，在理论上保证了此种方法的科学性，在证题的过程中可以看到此种方法是具有可行性的。

Furthermor, we consider their nondiferentiable situation, we define nonsmooth univex functions for Lipschitz functions by using Clarke generalized directional derivative and study nonsmooth multiobjective fractional programming with the new convexity. We establish generalized Karush-Kuhn-Tucker necessary and sufficient optimality condition and prove weak, strong and strict converse duality theorems for nonsmooth multiobjective fractional programming problems containing univex functions.

而且，本文利用Clarke广义方向导数针对Lipschitz函数在原来一致凸函数概念的基础上定义了不可微的一致凸函数，并利用这类新凸性，我们研究了非光滑多目标分式规划，获得了广义Karush-Kuhn-Tucher最优性条件；弱对偶定理、强对偶定理和严格逆对偶定理。

The strong and weak dual theorems are obtained in the sense of strictly efficiency in dual model which is established by scalar set-valued Lagrange mapping.

利用标量集值Lagrange映射建立了集值优化问题的对偶模型，并得到严有效性下的弱对偶和强对偶定理。

In view of these, the second part of this paper presents two sufficient conditions and two mixed type duals for the generalized fractional programming only under-convexity assumptions. These sufficient conditions apply to a broader class of mathematical programming problems.The results about weak duality, strong duality and strictly reverse duality arealso presented under more suitable conditions.

鉴于此，本文的第二部分，我们仅在函数—凸性假设下，给出了广义分式规划的二个最优性充分条件，这些充分条件较文献中的相关的条件有更广泛的适用性；同时还给出了混合型对偶，并且在适当的条件下，给出了相应的弱对偶定理、强对偶定理，以及严格逆对偶定理。

与对偶定理相关的网络解释 [注：此内容来源于网络，仅供参考]

dual system：对偶系统

dual spaces 对偶空间 | dual system 对偶系统 | dual theorem 对偶定理

dual theorem：对偶定理

dual system 对偶系统 | dual theorem 对偶定理 | dual vector space 对偶向量空间

dual vector space：对偶向量空间

dual theorem 对偶定理 | dual vector space 对偶向量空间 | duality 对偶性

duality theorem：对偶定理

对偶定理( Duality Theorem):加法对偶定理是一变数(A)与0执行逻辑加法(OR)运算,其运算结果都等於原来值(A). 乘法对偶定理是一变数(A)与1执行逻辑乘法(AND)运算,其运算结果都等於原来值(A).

strong duality theorem：强对偶定理

强度|strength | 强对偶定理|strong duality theorem | 强对偶空间|strong dual space

Pontryagin duality theorem：庞特里亚金对偶定理

庞特里亚金-范坎彭对偶定理|Pontryagin-van Kampen duality theorem | 庞特里亚金对偶定理|Pontryagin duality theorem | 庞特里亚金积|Pontryagin product

weak duality theorem：弱对偶定理

弱闭[的]|weakly closed | 弱对偶定理|weak duality theorem | 弱分歧扩张|tamely ramified extension

fundamental duality theorem：基本对偶定理

fundamental driving force 基本推动力 | fundamental duality theorem 基本对偶定理 | fundamental equation 基本方程式

Pontryagin-van Kampen duality theorem：庞特里亚金-范坎彭对偶定理

排中律|law of excluded middle | 庞特里亚金-范坎彭对偶定理|Pontryagin-van Kampen duality theorem | 庞特里亚金对偶定理|Pontryagin duality theorem

duality theory：对偶定理

"对偶单纯法","dual simplex method" | "对偶定理","duality theory" | "限交日期","due date"