在经过有限次迭代之后，可以求得原问题的最优解。
After a limited number of iterations, we can get the optimal solution of the primal problem.
将原问题分解为三个子问题：1．最优空车分配数；
The problem is decomposed into three subproblems:1. The number of optimal empty car distribution;
并将原问题的限制条件从不含数字4推广到不含任意个其他数字。
Moreover, the restrictive conditions of primary problem were extended from lack of'4'to lack of random number.
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.
由于边系统仅含单参数，这样就大大地降低了原问题的计算复杂性。
Since a so-called edge system contains only one parameter, the computational complexity of the original problem will be reduced to a...
任何有效的近似式必须在某种意义上提供一个接近于原问题解的结果。
For any approximation to be valid it must provide a result that is in some sense close to the solution of the original problem.
通过研究截断问题的弱解，我们证明了原问题存在一列非平凡的小解。
By investigating the truncated problem, we could prove that the original problem admits a sequence of small solutions.
并且建立了原问题的K-T点与等价无约束问题的稳定点之间的关系。
Moreover, we get the relationship between the K-T point of the primal problem and the stationary point of the unconstrained problem.
并通过变量代换，将原问题的非齐次边界条件转化为齐次边界条件的边值问题。
Through the change of variables, the original problem with inhomogeneous boundary condition is reduced to the boundary value problem of homogeneous boundary condition.
用该近似函数形成结构优化原问题的序列近似问题，再用约束变尺度法解近似问题。
The improved approximate expressions are proposed to create the sequential approximation problems which are solved with the constrained variable metric method.
集成策略的基本思想是把原问题分解为一系列的子问题，并采用合适的方法优化之。
The main idea of integrated strategies is to make the original problems be a series of sub- problems and choose appropriate method for optimization.
本文研究了具有边界摄动的抛物型方程。利用可解性的讨论，得到了原问题的摄动解。
In this paper, the parabolic equation with boundary perturbation is considered. Using discussion of the solvability, the perturbed solution of original problem is obtained.
本算法对原问题的形式无特殊要求，可推广求解一般的高维相关性强的线性规划问题。
Compared with other decomposition algorithm, it does not demand the original linear program ming to have a particular structure and it can be used to solve line…
着重讨论分层结构中的流率控制层，论述了前人给出的求解原问题的一些工程近似想法。
The flow rate control level is focused and the simple engineering approximation of the original problem proposed by other scholars is discussed.
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.
同时，本文还分析了制约梯级水电站各个因素，将原问题化为一个有约束非线性规划问题。
Besides, this paper have analyzed factors that restrict multi-reservoir system power station, and turn former problem into retrained non - linear planning problems.
最后，将原问题的减缩解映射回原空间，在保证了效率和精度的前提下得到了原系统的近似解。
After the Galerkin projection of matrices into the reduced basis space, a reduced system was obtained and can be solved efficiently. The reduced solution was obtained.
该方法采用分解策略，将原问题分解为一系列两类分类问题，降低了训练规模，提高了训练速度。
The classification method USES decomposition strategy to decompose initial problem into a series of two-class classification problems that reduces training scale and enhances training speed.
提出一种新的在线逆散射方法—支持向量机，通过支持向量机将原问题转化成一个回归估计问题。
In this paper, a new online methodology is presented for the solution of inverse scattering problems.
所给方法利用状态分解将原问题转化为一组设备控制器的耦合决策问题，以简化单个控制器的求解空间。
The presented algorithm simplified the state space by converting the original problems into coupling decision processes of several cooperative local controllers.
当非退化条件成立和磨光参数趋于零时，证明了原问题的S -稳定点与磨光非线性规划的KKT点等价。
As the non-degeneracy condition holds and the smoothing parameter tends to zero, an S-stationary point of the MPCC problem is equivalent to a KKT point of the smoothing nonlinear programming.
沿袭用锥模型来逼近原问题的思路，本文主要研究锥模型拟牛顿信赖域方法的参数选择、收敛性和数值实现。
In this paper, we mainly discuss the modified quasi-Newton trust region methods based on a conic model (TRCM method) and prove their convergence properties.
该模型求解时，首先通过引入代理函数将原问题解耦为残差的加权范数最小化和加权范数TV去噪这两个子问题；
Using surrogate function, we split the sum minimization scheme to the minimizing weighted least square function and TV denoising with weighted norm iteratively.
环境中能够刺激机体发生过敏反应的都可称为过敏原，我们每天接触的食品中的过敏原问题也是一项不容忽视的问题。
Anaphylactogen can stimulate bodies and force the body to response. Anaphylactogen from foods can also bring diseases, it becomes an important problem in society.
在无功优化计算中，由于严格的节点电压限制、网络拓扑的变化或无功电源的不足等多种原因可能会导致原问题不存在最优解。
In reactive power optimization, the solution infeasibility may arise due to a variety of reasons such as restrictive voltage limits, change in network topology, and shortage of reactive power sources.
因此可先在粗尺度上迭代反演，得到一个较好的参数估计，再将这个估计作为较精细尺度的初值进行反演，直至原问题的全局最优解。
So firstly to get a better estimation of parameter using iterate inversion on wide scale, then using this estimation as initial value on mini scale till to get global optimum of original problem.
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.
利用牛顿方向和中心路径方向，获得了求解单调线性互补问题的一种内点算法，并证明该算法经过多项式次迭代之后收敛到原问题的一个最优解。
By using Newton direction and centering direction, we establish a feasible interior point algorithm for monotone linear complementarity problem and show that this method is polynomial in complexity.
利用牛顿方向和中心路径方向，获得了求解单调线性互补问题的一种内点算法，并证明该算法经过多项式次迭代之后收敛到原问题的一个最优解。
By using Newton direction and centering direction, we establish a feasible interior point algorithm for monotone linear complementarity problem and show that this method is polynomial in complexity.
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