对偶理论

多目标规划的Hα-共轭对偶理论

H_ α - Conjugate Duality Theory in Multiobjective Programming

多目标广义分式规划的Lagrange最忧性条件和对偶理论

Multiobjective generalized fractional programming : lagrange optimality conditions and duality theory

三种度规下Maxwell方程的双矢势对偶理论

Two Potential Duality Theory of Maxwell Equation under Three Metrics

双荷粒子Lorentz力的双矢势对偶理论

Two potential duality theory of Lorentz force of dyons

（F，a，p，d）-凸性下向量极值问题的最优性条件和对偶理论及非线性多目标规划问题的一个算法

The Optimality Conditions and Duality Theory for Vector Extremum Problem under ( F , a , p , d ) - Convexity & an Algorithm for Nonlinear Multi-objective Programming

最优化问题的Lagrangian对偶理论与SQP方法

Lagrangian Dual Theory and SQP Method in Optimization Problem

在PERT技术中运用对偶理论，为敏度分析创造了必要条件。

Prerequisite for dual theory and sensitivity analysis in PERT is set up .

最后，利用双层规划的对偶理论，给出求解OEM业务最优策略的一种多项式时间算法。

Finally a polynomial-time algorithm for the optimal strategy of OEM is gotten by using dual theory of bilevel programming .

一类不可微规划的Kuhn-Tucker充分条件及其对偶理论

Sufficiency of the Kuhn-Tucker condition and dual theories for a class of nonsmooth optimization

对于求解这类一般变分不等式问题的基于增广Lagrangian对偶理论分解算法，本文给出了算法的收敛性分析。

We propose a general decomposition algorithm based on the augmented Lagrangian for solving this complex general variational inequality problems with the coupling constraints .

低速Dyon粒子电磁辐射的双矢势对偶理论

Two potential dual theory of EM radiation for low speed moving Dyons

高能Dyon粒子电磁辐射的SO（2）对偶理论

SO ( 2 ) Duality Theory of EM Radiation of High Energy Dyons

Gal所做的工作基础上，应用矩阵理论和对偶理论，对技术矩阵A含线性参数的参数线性规划问题进行了讨论。

Gal , through matrix theroy and dual theroy , the auther deals with a problem concerning a linear parametric programming ( LPP ) of A-matrix with linear parameters .

其次，将对偶理论应用到典型实例圆柱管道中的Bingham流体问题中，为数值求解带来了方便。

Secondly , the duality theory will be applied to typical examples of the Bingham fluid problem in cylindrical pipe , which takes the advantage for the numerical solution .

藉助于凸规划的Lagrange对偶理论，建立了Mises屈服条件下理想刚塑性材料Hill最大塑性功原理的对偶问题，并据此建立了极限分析的一个不可微凸规划模型。

By means of Lagrange duality theory of the convex program , a dual problem of Hill 's maximum plastic work principle under Mises ' yielding condition was derived and whereby a non-differentiable convex optimization model for the limit analysis were developed .

第二章利用分式对偶理论和Kuhn-Tucker条件，给出了双层线性分式规划的最优性条件，并且设计出行之有效的算法。

In the second chapter , bilevel linear fractional programming problem , in which the constraint region is polyhedral , is discussed . Several optimality conditions are derived based on dual fractional program and Kuhn-Tucker conditions . An efficient method is given with the help of the PCP algorithm .

利用Fenchel对偶理论将大规模凸优化求解问题转化为中小规模凸优化求解问题。（2）给出了基于Fenchel对偶分解原理的KLR分类并行算法的软件实现。

The main idea is translating large scale convex optimization problem into lots of small scale convex optimization , using the Fenchel Duality theory . ( 2 ) Given the software of the parallel solver for kernel logistic regression classification algorithm based on the Fenchel Duality theory .

针对C2R模型下决策单元在输入和输出的不对称性以及新的线性等价形式在对偶理论上的不足，引进了C2R新线性等价形式的对称模型，并论证了该模型的合理性。

This note introduces a symmetric models for the unsymmetric problems of new linear equivalent form of C ~ 2R models and the shortcomings of new linear equivalent form of C ~ 2R models in dual theory , and shows that the symmetric models of C ~ 2R is reasonable .

应力函数及其对偶理论在有限元中的应用

Application of stress functions and its dual theory to finite element

局部凸空间上的可分解算子及其对偶理论

Decomposable Operators on a locally convex space and their duality theory

应用对偶理论求解二次规划问题的一种方法

An Application of the Dual Theory to Solve Quadratic Programming

建立了基本二元关系以及偏好关系的对偶理论。

This paper establishes the duality theory of preference relations .

一类灰线性规划及其对偶理论研究

Research on a kind of grey linear programming and their dual theories

模糊线性规划对偶理论研究及算法

Study on Duality Theory in Fuzzy Linear Programming and Algorithms

电四极和磁四极辐射的SO（2）对偶理论

SO ( 2 ) Duality Theory of Electric Quadrupole and Magnetic Quadrupole Radiation

基于对偶理论的消费者行为选择问题研究

Research of Consumer Behavior Choice Based on Duality Theory

电磁场能量动量张量的双矢势对偶理论

Two potential dual theory of EM field energy-momentum tensor

一般形式多阶段有补偿问题的广义对偶理论

Generalized Duality Theory on the General Multistage Recourse Problem

再次，我们回忆了向量集值优化问题解的有效性和对偶理论。

Thirdly , we recall efficiency and duality theory of vector set-valued optimization problems .

一类η-凸多目标规划的最优性必要条件和对偶理论

The Optimality Necessary Conditions and the Duality of a η - convex Multi-objective Programming