无约束的

Based on the concepts of complex product, standard operation, virtual operation, no-wait and the expansion processing tree defined in this paper, the standard operations are processed by allied critical path method and best fit scheduling method, and the virtual operations are processed respectively on corresponding machine with movement and exchange algorithm in order to translate scheduling problem with no-wait operations into the general scheduling problem with virtual operations.

该方法在提出复杂产品、标准工序、虚拟工序、零等待和扩展加工工艺树的概念基础上，对扩展加工工艺树中的标准工序采用拟关键路径法和最佳适应调度的车间调度算法进行调度，对虚拟工序采用移动交换算法在相应设备上分离调度，将存在零等待约束的调度问题转化为存在虚拟工序的无零等待约束的调度问题。

On the basic that existing second-order sufficient condition for an isolated minimizer of order 2 for unconstrained multi-objective optimization, using the so called oriented distance from a point to a set, l-stable function and generalized second-order Peano direction derivative, some second-order sufficient conditions for an isolated minimizer of order 2 for constrained multiobjective optimization problems with l-stable functions are obtained.

在已有的无约束l-稳定函数多目标优化问题的二阶充分条件的基础上，借助定向距离函数和l-稳定函数的性质及引入的广义二阶Peano方向导数，进一步刻画了具有抽象约束的l-稳定函数的多目标优化问题的二阶孤立极小点的二阶充分条件。

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 hypotheses,the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem.

在适当的假设下，给出了原约束问题的局部极小点与增广Lagrange函数，在原问题变量空间上的无约束局部极小点之间的对应关系。

Until recently, the convergence of the Rosen"s arithmetic has been proved. The projection gradient method is the generalization of Steepest decent method to constraint problem. So it does have a faster convergence speed that the fastest decent method . To solve the problem, many researchers have generalizat the well-developed optimization with unconstraint to the Rosen"s gradient method. The conjugate gradient method is one of success to solve the problem.

投影梯度法是最速下降法对约束问题的推广，因此没有较快的收敛速度，为了解决这个问题很多中外学者把发展得比较成熟的无约束最优化算法作类似的推广，其中共轭梯度方法是近年发展的很成熟的方法，它具有计算简单，算法结构好，计算量少，具有良好的收敛性等优点，而Rosen投影梯度法的提出使寻找下降方向变得简单。

By using generalized projection matrix, conditions are given on the scalars in the three term-memory gradient direction to ensure that the three term-memory gradient projection direction is a descent direction. A new three term-memory gradient projection method for nonlinear programming with nonlinear equality and in-equality constraints is presented.

利用广义投影矩阵，对求解无约束规划的三项记忆梯度算法中的参数给一条件，确定它们的取值范围，以保证得到目标函数的三项记忆梯度广义投影下降方向，建立了求解非线性等式和不等式约束优化问题的三项记忆梯度广义投影算法，并证明了算法的收敛性。

In the western mining areas, when from adjustment to restriction adjustment, the original national control points are of low grade, or the points are destroyed and the surface movement is out of shape. thus, there are few control points and the reference frame conversion is a big problem in the western high elevation areas. As a result, this thesis makes a reparable design in accordance with the key problems of holing through survey.

本文就利用GPS技术测设地面近井点的网形布设、观测方法、数据处理作了相应阐述；并对由无约束平差到约束平差时，西部地区可能遇到在矿区分布的原有国家控制点往往只有低等级点，或点位遭破坏、地表移动变形等可能使可用控制点很少的情况、以及西部高海拔地区坐标系统变换问题，提出了针对贯通测量的关键问题应对方案。

To solve the difficulties of digital integral that exist in global optimization of redundant manipulators, this paper discussed how to build up dynamic equation, the inner relation between constraints and unconstraint optimum control problems, then a digital method solving optimum control problems is deeply analyzed.

为了解决冗余度机器人全局法优化中数值求解的困难，本文讨论了动力学方程的建立、无约束和有约束最优控制问题之间的内在联系，重点分析了求解最优控制问题的数值方法。

Through adding new state variable and using supplement functions,the problem with restriction conditions was converted into nonrestriction problem.

通过增加新的状态变量和用补偿函数法，将本课题的有约束条件问题化为无约束条件问题，并提出了最优步长参数的动态搜索法来修改传统的梯度法，从而较完善地解决了多变量最优周期控制的计算问题。

Through adding new state variable and using supplement functions,the problem with restriction conditions was converted into nonrestriction problem.In addition,the dynamic searching method of optimal step coefficient was developed to modify the conventional gradient method,consequently the calculation problem of the multivariable optimal periodic control was able to be resolved better.

通过增加新的状态变量和用补偿函数法，将本课题的有约束条件问题化为无约束条件问题，并提出了最优步长参数的动态搜索法来修改传统的梯度法，从而较完善地解决了多变量最优周期控制的计算问题。

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。