投影梯度法

First, a special normal transversal at the initial point is constructed and a second-order Taylor's algorithm is used to trace the projections along the aforementioned normal transversal. A curvature based method for controlling iteration step is further proposed by projecting the given point onto the curvature circle of the normal transversal at the initial point. Finally gradient based method for correcting iteration errors is put forward.

首先构造初始点处的一条特殊的法截线，并给出沿着该法截线追踪投影点的二阶泰勒迭代方法；然后将给定点向初始点处的法截线的曲率圆作投影，提出基于曲率的步长控制策略，在此基础上给出了基于梯度的迭代误差矫正方法。

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。

A new weighted mean algorithm according to angle vector is presented for modifying multipoint interference of tool axis.

该算法采用投影法，计算负梯度方向的搜索步长，快速计算出刀具中心线与曲面、刀具端面与曲面之间的最短距离。

First, we extract the boundaries between two different materials by weighting with gray-level gradient,and only voxels on these boundaries participate in the generation of each image, so it drastically reduces the rendering time. Second. We think the voxels on boundaries as the mixture of different materials,so in every voxel there is a surface. We use the oriented cube-interpolation technique to get the intersection point of viewing orientation and the surface in the voxel, then compute the surface normal of the intersection point. We use the normal to shade the voxel in order to improve the image quality.

首先，采用灰度梯度加权提取出三维数据场中不同物质间的边界，根据显示的需要只对这些边界上的体元赋予相应的阻光度并进行光亮度合成计算，因而可大大减少计算量，提高显示的速度；将边界上的体元作为不同物质的混合体，采用与方向有关的三线性插值来计算视线方向与体素内等值面的交点，根据交点的法向量进行光照效应计算以提高显示图像的质量；最后用投影成像法显示最终的图像。

The gradient projection method is a class of effective algorithms for constrained optimization problem,and it has an important position in optimization.

梯度投影法是一类有效的约束最优化算法，在最优化领域中占有重要的地位。

Best [25] appears to be the first to suggest the use of Rosen's gradient projection method [154] for optimal structural design.

最好[25]看来是建议使用的第一个Rosen's梯度投影法[154]优选的结构设计的。

But the projection used in gradient projection method is an orthogonal projection which does not contain the second derivative information of objective and constrained functions,thus the convergence rate of gradient projection method is not contented.

但是，梯度投影法所采用的投影是正交投影，不包含目标函数和约束函数的二阶导数信息·因而；收敛速度不太令人满意。

For the optimization of the continuous variables, the author combines the weaken idea, the DFP and the gradient projection method to form a modified Goldfarb method by which the optimal problems of the trusses can be solved.

对于连续变量优化，作者将松弛思想、变尺度公式和梯度投影法相结合，建立了一种专门解决杆系优化问题的修正Goldfarb法，算例计算表明本法是针对性强、效率高的优化算法。

Firstly, an Iterative Closest Point algorithm is applied for coarse registration. Secondly, gradient feature is extracted from image. Based on the principle of projective transformation, the fine registration is performed by finding the maximum CT gradient projections.

首先基于一种最近点迭代法进行快速粗配准；然后提取图像的梯度特征，根据投影变换原理，采用寻找具有CT最大梯度投影位置的方法进行精配准。

A proper k total colouring of a graph G is a colouring to its vertices and edges using k colours such that no two adjacent or incident elements of G may be assigned the same colour.

利用梯度投影与罚函数相结合的技巧，将带不等式和等式约束的优化问题化成一个无约束问题，提出了初始点可任意的求解不等式、等式约束优化问题的摄动梯度投影算法；参数δk取不同的数还可以得到一类梯度投影算法，从而得出了在搜索方向和步长不精确条件下的梯度投影法，保证了在实际应用中更容易实现；在较弱条件下，证明了该算法的全局收敛性。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。