约束变量

Moreover, it makes the coefficient matrix of centralized IPM's linear correction equation a block diagonal bordered matrix, which can be decomposed into the constraints equation on internal variables of independent sub-areas and coupled constraints equation. During each IPM iteration, internal variables and coupled variables are solved distributedly; thus distributed algorithm of multi-area ORPF is implemented.

在此基础上，论文将该线性方程分解为相互独立的子区域内部约束方程和复制节点的耦合约束方程，在每次内点法迭代中分布分块求解内部变量和耦合变量，从而实现多区域无功优化的分布式计算。

The forward kinematics is analyzed by choosing one of the mechanisms which have one, two,three or zero angle constraint.Wherein,3-CCC is a new parallel mechanism which has three angle constraints and three distance constraints, Calay\'s formular and direction cosine matrix are used to describe the rotation matrix respectively.By setting Dixon\'s and Sylvester\'s resultant with the three angle constraint equations respectively and using parameters replacement to deal with the distance constraint equations,the 64 order input-output equation of the forward kinematics is obtained under both of the methods.Numerical example confirms these theretical results and the motion simulation is shown in VC++ by integrating OpenGL.

3对高小山提出的广义并联机构进行了研究，以其中具有角度约束的并联机构进行了分析，选取具有一个、两个、三个和零个角度约束类型中各一个机构进行了运动学正解求解，其中3-CCC是一种全部由圆柱副构成的具有三个线线角度和三个距离约束的新型并联机构，文中分别用Calay公式和方向余弦两种旋转矩阵建模方法对其位置正解进行了分析，通过对三个角度约束方程分别构造Dixon结式和Sylvester结式，以及对三个距离约束方程进行变量代换分别导出了位置正解输入输(来源：4040ABC论文网www.abclunwen.com)出方程，得出64组位置正解，并使用数值算例验证了其全部根。

This algorithm constructs a set of linear equations. As a result, the relation of the reconstructed design variables and the original design variables is derived, the variable number of optimum design is decreased from m + n + 2 to 4, and the equality constraint optimization problem is converted into reduced- dimension no equality constraint optimization problem.

该算法通过构造一组线性方程，得到了由重构设计变量到原设计变量的映射关系，使优化设计的变量由原来的m + n + 2个减少到4个，并将有等式约束优化问题转换成降维的无等式约束优化问题。

Constraint analysis method can divide variables in a constraint system into four types: underconstrained variable, full-constrained variable, over-constrained variable, free variable, and related algorithm is presented.

预处理分为三个步骤：约束分析、冲突化解和求解规划。约束分析可以判断出约束系统中的冗余约束和变量的约束类型。

Regarding iterated processes as objective function,parameters of algebra iterated system as design variables,and boundary condition of iterated variables as constrains,a new optimum method was proposed,which was used to calculate bifurcation of Logistic mapping.

以迭代过程关系构成目标函数，参数为设计变量，迭代变量的边界为约束，建立关于分支值计算的新方法含约束条件的最优化程序算法。

By redefining multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse the method dedicated to equality constraints for constructing Lagrange neural networks.

若重新定义与不等式约束相关的乘子为正定函数，则在构造Lagrange神经网络时，可直接使用处理等式约束的方法处理不等式约束，不需再用松驰变量将不等式约束转换为等式约束，减小了网络实现的复杂程度。

Therefore, from the theoretical point of view, a solution of the constrained problem and the corresponding values of the Lagrange multipliers can be found not only by the well known method of multipliers but also by performing a single unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the product space of problem variables and multipliers.

因此，从理论的观点来看，原约束问题的解和对应的拉格朗日乘子值不仅可以用众所周知的乘子法求得，而且可以通过对Hestenes-Powell增广拉格朗日函数在原问题变量和乘子变量的积空间上执行一个单一的无约束极小化来获得。

Under suitable assumptions, the relationship is established between the unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the space of problem variables and the solution of the original constrained problem, and a relationship is also presented between the unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the product space of problem variables and multipliers and the solution of the original constrained problem.

在适当的条件下，我们建立了Hestenes-Powell增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系，并且也给出了Hestenes-Powell增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系。

It can be integrated into existing applications. It is designed for application developer. The system provides power modeling. Users can widely select decision variables, such as integer, real, Boolean, etc. Users can also select extensive set of predefined constraints, such as primitive constraints and function constraints, local constraints and global constraints.

"明月"系统是开放的C++类库，可嵌入到具体的应用中，可扩展，是面向开发人员设计的；系统具有强有力的建模功能，用户可以广泛选择决策变量，例如整型、实型、布尔型等；可扩展的预定义约束集合，其中包括基本约束和功能约束，局部约束和全局约束。

In this paper, the Hestenes-Powell augmented Lagrangian function is again considered, for solving equality constrained problems via unconstrained minimization techniques.

在适当的条件下，我们建立了Hestenes-Powell 增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系，并且也给出了Hestenes-Powell 增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。