梯度法

The results were as follow: At fine, cloudlet and cloud weather in rainy season,the mean value of CO 2 content varied in a range of 349 to 350ml/m\+3 at 2.8m above the canopy, 346 to 348ml/m\+3 at 0.8m above the canopy, 345 to 349ml/m\+3 at 16m inner the forest and 352 to 357ml/m\+3 at 5m above ground in the period from 9:00 to 18:00.The CO 2 content in rainy season was lower than that in dry season. At the same weather and space-time, CO 2 content in rainy season was higher than that of CO 2 in dry season at both day and night. According to the grads calculation, there were the CO 2 flux from atmosphere to canopy with 0.61×10 -6 and 0.71×10 -6kg/(m 2·s) during day time in dry and rainy seasons respectively.

采用梯度法及CI-301PS CO2系统，实现了海南尖峰岭热带山地雨林近冠层CO 2、微气象因子梯度观测研究，结果表明：雨季晴、晴间少云及多云天气，9：00～18：00CO 2浓度平均值分别在349～350ml/m3(冠上2.8m)、346～348ml/m3(冠上0.8m)、345～349ml/m3(林内16m)、352～357ml/m3(林内5m)，较旱季相应天气分别小14～17.5、10.1～23.7、1 6.4～35.7和18.1～36.1ml/m3；1：00～8：00，则雨季CO2浓度大于旱季；梯度浓度廓变量和实时动力计算反映出，8：00～18：00CO2通量由大气向林冠层，旱、雨季平均CO2通量分别为0.61×10-6kg/(m2·s和0.71×10-6kg/(m 2·s)，19：00通量甚微，20：00～7：00CO2通量则由林冠向大气，平均CO2通量分别为0.36×10-6kg/(m2·s)和0.32×10-6kg/(m2·s)；雨季昼夜大气流向冠层的净CO2通量是相应旱季的1.56倍。

The content of our curriculum are:Optimization under unconstrained conditions and constrained conditions,we'll focus on common methods of this field like Conjugate gradient method,DFP,POWELL method,The multiplier method,Penalty Function Method and so on.

主要讲授内容为无约束条件及有约束条件下的优化设计，重点介绍了共轭梯度法，变尺度法，POWELL法，乘子法，惩罚函数法等电路优化的常用方法。

By means of the projection method,adding a small disturbing function to the objective function, the penalty method, andthe gradient method, this dissertation proposes several neural networks for solvingsaddle point problems and minimum radius of ball-coverings problems, and investi-gates the stability of the proposed networks by the LaSalle invariance principle andthe Lyapunov method, so as to design neural networks which avoid getting stuck inthe local minimum.

本文针对约束鞍点问题和球覆盖最小半径的计算问题，分别利用投影法、对目标函数加上很小"扰动函数"的逼近法、罚函数法和梯度法等建立神经网络模型进行求解，并基于LaSalle不变集原理和Lyapunov直接法等工具，对模型的动态特性进行研究，从而设计出避免陷入局部极小的优化计算神经网络模型。

The reconstruction problem is ill-posed, so two optimal criterions, the least module and the smoothness criterion base on Tikhonov regularization technique, are introduced into reconstruction algorithm. Many regularization parameters choice strategies are investigated, and the TPA(Two—Parameter Algorithm) strategy which is based on the Morozov discrepancy principles, is implemented in two regularization reconstruction algorithms.Numerical experiment results show that the nonnegative and smoothness constraint condition can overcome the difficulty of iteration semiconvergent, preconditioned technique can improve convergence rate and reconstruction accuracy, smoothness regularization criterion can meliorate ill-posed problem of reconstruction and enhance iteration stability, and the TPA is an effective strategy of regularization parameters choice.

数值试验表明：在共轭梯度法中引入非负约束和光滑约束改善了迭代的"半收敛"性，非负约束保证了解的非负性，光滑约束抑制了重建解的振荡现象，约束算法的重建精度与无约束算法相比大幅度提高；在约束共轭梯度重建算法中引入预优技术，可以加快算法的收敛速度，提高迭代的稳定性和重建精度；引入光滑准则的正则化技术可以有效改善图像重建问题的不适定性，加快迭代的收敛速度，提高迭代的稳定性和图像重建质量，计算正则参数的TPA算法在闪光照相图像重建中是有效的。

Then depended on the Gradient Projection Method, the gradient projection direction is deduced. The gradient direction is the basement for sensitivity analysis.

接着，根据投影梯度法，推导出了投影梯度方向，该方向是灵敏度分析的基础。

We transforms the special linear system of strict inequalities into three kinds of minimax problems, and then solves it with the aggregate function method assisted with some corresponding method. At last the numerical experiment is done under the environment of matlab.

我们将其转化为三种形式的Minimax问题，对转化后的三种Minimax问题，用凝聚函数法分别将其目标函数光滑化，并分别用带Armijo不精确线搜索的最速下降法、带自适应参数修正的凝聚函数法以及既约梯度法来求解。

With the guide of non-linear program theory, by using interpolative steps and inexact line search, an improved conjugate gradient method was found, by which the training rate of BP networks increases by tens or hundreds of times. Moreover, the improved method is effective to solve non-linear equations for which Newton's method does not converge owing to the problems of the quadratic derivative and inverse matrix.

通过大量的数值模拟试验发现，在非线性规划理论的指导下采用间插步骤和不精确的一维搜索技术改进的共轭梯度法，是基于梯度和共轭方向的连续搜索算法中最有效的算法，这种算法使BP网络的训练速度提高几十到几百倍，使BP网络的实际应用效果大为改善；而且这种算法对于用牛顿法由于求二阶导数和求逆矩阵等问题难于收敛的非线性方程组的求解也是很有效的。

The reconstruction problem is ill-posed, so two optimal criterions, the least module and the smoothness criterion base on Tikhonov regularization technique, are introduced into reconstruction algorithm. Many regularization parameters choice strategies are investigated, and the TPA(Two—Parameter Algorithm) strategy which is based on the Morozov discrepancy principles, is implemented in two regularization reconstruction algorithms.Numerical experiment results show that the nonnegative and smoothness constraint condition can overcome the difficulty of iteration semiconvergent, preconditioned technique can improve convergence rate and reconstruction accuracy, smoothness regularization criterion can meliorate ill-posed problem of reconstruction and enhance iteration stability, and the TPA is an effective strategy of regularization parameters choice.

数值试验表明：在共轭梯度法中引入非负约束和光滑约束改善了迭代的&半收敛&性，非负约束保证了解的非负性，光滑约束抑制了重建解的振荡现象，约束算法的重建精度与无约束算法相比大幅度提高；在约束共轭梯度重建算法中引入预优技术，可以加快算法的收敛速度，提高迭代的稳定性和重建精度；引入光滑准则的正则化技术可以有效改善图像重建问题的不适定性，加快迭代的收敛速度，提高迭代的稳定性和图像重建质量，计算正则参数的TPA算法在闪光照相图像重建中是有效的。

It includes two aspects in content: one is the best choice for plane disposal of pipeline, and its methods follows as decision-making plot, simple trapeziform and optimizing trunkform etc; the other one is optimizing pipe parameter when the plane disposal of pipeline has been fixed, and the methods of which are linear programming, unlinear programming, dynamic optimizing, direct optimizing, hereditary arithmetic and so on.

污水管网优化设计包括两个方面的内容：一是管线平面布置的优化选择；其方法有：决策图法，简约梯度法，优化树法等。二是在管线平面布置已定情况下进行管道参数的优化；其方法有：线性规划法，非线性规划法，动态优化法，遗传算法，直接优化法等。

Gradient ca lculator com bines GA and Gradient Algorithms very well and improves searching speed and prec ision obviously.

梯度算子的引入，将梯度法和GA很好地融合了起来，大大提高了GA的搜索精度和速度，收到了令人满意的效果。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。