运输模型进一步讨论，运输对偶问题分析，本章小节。
Further discussions about the transportation models, analysis on the dual transportation problems, summary of the Chapter 3.
主业联合重组的对偶问题是非主业产业的资本运营问题。
Union and reorganization of principal industry directly results in the question of non-principal industrys capital operation.
集合覆盖问题的各种变体以及其对偶问题的随机算法研究。
Randomized algorithms for the set cover problem and its variations and duals.
然后依据对偶问题的解，以启发式方法构作原问题的可行解。
A heuristic method is then proposed to construct a feasible solution of the original problem.
在这个意义上最大化问题会被称为初始问题，最小化问题就称为对偶问题。
The maximization problem is then called the primal problem, and the minimization is the dual problem.
分析了广义矩问题及其对偶问题的关系，获得了求解广义矩问题的方法。
This paper analyzes the relation between the generalized moment problem and its dual problem, and gives the solution to some generalized moment problems.
本文对半无限凸规划提出一个用方向导数表述的对偶问题，其对偶间隙为零。
The paper offers a dual problem for the semi-infinite convex programming by using the directional derivative with zero dual gap.
根据对偶理论，应用对偶规划精确映射原问题，再按泰勒展式建立对偶问题的二阶近似。
According to the dual theory, the dual programming was used to map the original problem exactly and the second approximation of the dual problem was set up by Taylor's expansion.
在第六章中，我们考虑对偶问题，基于对偶建立几个计算程序，并讨论了参数和灵敏度分析。
In Chapter six we consider the dual problem, develop several computational procedures based on duality, and discuss sensitivity and parametric analysis.
分析了随机最优化领域中广义矩问题及其对偶问题的关系，从而提出了广义矩问题的一种新的求解方法。
Analyzes the relation between the generalized moment problem and its dual problem, and gives a new method for solving some generalized moment problems.
运输问题的数学模型及其特征，运输问题的求解方法（表上作业法），运输模型的进一步讨论，运输模型对偶问题分析。
The transportation models and its characters, the Transportation Simplex Method, Further discussions about the transportation models, analysis on the dual transportation problems.
运用子梯度方法求解新模型的对偶问题，得到了一种新的基于对偶问题的分布式算法框架，并证明了这种新算法的收敛性。
Through analyzing the characteristic of the source algorithms and AQM at the equilibrium, we propose a new model with less constraint condition and a distribution algorithm with larger application.
采用椭球剖分策略剖分可行域为小的椭球，用投影次梯度算法解松弛二次规划问题的拉格朗日对偶问题，从而获得原问题的一个下界。
A projection subgradient algorithm for the Lagrangian dual problem of the relaxed quadratic problem is employed to general lower bounds of the optimal value for the original problem.
并研究了原问题的最优解和对偶问题的最优影子价格的关系，当原问题有最优极方向时，它的最优解不一定是对偶问题的最优影子价格。
The optimal solution of the original problem was not certainly the optimal shadow price of its dual problem when the optimal extreme directions of the original problem were in existence.
结果表明这个问题没有对偶的可行方案，不过这是什么意思呢？
It says that the problem has no dual feasible solution, but what does that mean?
每个问题都有对偶性。
我思考了一下，我可能会,描述成一部分是冒险家，一部分是问题解决者，一部分鲜明的个性，有那么点偏执，还有那么点反对偶像崇拜。
I put some thought to this and I would describe it as probably part adventuralist, part problem-solver, part ejecable traits, sort of a touch of maverick, sort of a touch of iconoclast.
文中引入了一类广义不变凸函数，对一类变分问题给出了最优解的充分性条件以及对偶理论。
The generalized invex functions are introduced and the optimality theorems and duality theory are established for a class of variational problems.
本文给出了强魔性对偶矩阵和矩阵平移积的新概念；研究了这类矩阵的计数问题。
Some new concepts on strong magic dual matrix and matrix translation product are given and counting problem of these matrices are then studied.
针对横观各向同性弹性柱体问题构造了对偶体系。
The duality system is introduced for the problem of elastic cylinders with transverse isotropy.
研究了对偶带宽问题的基本性质和计算复杂性。
An introductory study of the dual bandwidth problem is presented.
第3章给出无约束极大极小问题的一个对偶算法的收敛理论。
Chapter 3 is devoted to the study of the convergence theory of a dual algorithm for unconstrained minimax problems.
对变量组合法进行了改进，使多困难度几何规划中对偶变量分离问题简单易解。
The improvement to the method of variable combination makes the problem of dual variable separation in geometric programming with a multi difficulty degree simple and easy to solve.
对于有大量变量的问题，原始对偶算法将更为有效。
In case of problems with thousands of variables, the primal-dual algorithm will be far more efficient.
通过引入对偶变量，将平面正交各向异性问题导入哈密顿体系，实现从欧几里德几何空间向辛几何空间的转换。
Based on the dual variables, the Hamiltonian system theory is introduced into plane orthotropy elasticity, the transformation from Euclidian space to symplectic space is realized.
此公式具有渐进强对偶的特性并且可以保证找到原问题的最优解。
This formulation possesses an asymptotic strong duality property and guarantees a success for identifying an optimum solution.
一种基于线性规划及对偶分析的战场物资运输的指挥控制方法为解决此类问题提供了一种可行途径。
This paper proposes a command and control method of the battlefield materials transportation, which is based on linear programming and dual analysis.
首先回顾了采用最钝角行、列主元规则求解线性规画问题的原始、对偶可行解的主要过程，阐述了其与众不同的特性。
First, the main procedures and the distinctive features of the most-obtuse-angle (MOA) row or column pivot rules are introduced for achieving primal or dual feasibility in linear programming.
然后，运用凸优化技术分析了该资源分配问题，并基于拉格朗日对偶法给出了一种子载波和功率最优分配算法。
Then, by use of multiple carrier system's frequency-sharing property and convex optimization, a subcarrier and power optimal allocation algorithm is proposed based on Lagrangian duality theory.
然后，运用凸优化技术分析了该资源分配问题，并基于拉格朗日对偶法给出了一种子载波和功率最优分配算法。
Then, by use of multiple carrier system's frequency-sharing property and convex optimization, a subcarrier and power optimal allocation algorithm is proposed based on Lagrangian duality theory.
应用推荐