查询词典 projection gradient method

The projection gradient method will be a possible way to solve the problem that we just get. It has been shown that the projections of the every directions, of which is the boundary point in linear restraint problems, are the possible decent directions, and the projection of negative grads direction is a decent direction. In 1960, Rosen proposed the basic idea of projection gradient methods, and then lots of researchers have been tried to find the convergence of this method. But most of them get the convergence with the condition to amend the convergence itself.

在约束最优化问题的算法中怎样寻找有效的下降方向是构造算法的重要内容，在寻找下降方向方面可行方向法中的投影梯度法有效的解决了下降方向的寻找问题，利用线性约束问题边界点的任意方向在边界上的投影都是可行方向，而负梯度方向的投影就是一个下降方向。60年代初Rosen提出投影梯度法的基本思想，自从Rosen提出该方法以后，对它的收敛性问题不少人进行了研究，但一般都是对算法作出某些修正后才能证明其收敛的，直到最近对Rosen算法本身的收敛性的证明才予以解决。

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。

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。

The first section is descriptive geometry, including basic knowledge of cartography and projection, projections of point, beeline, plane and their interrelations, projection transformation, curve, curving plane, the projection of curving plane solids, line of section, line of intersection, section and segmentation, elevation projection, dimetric projection.

第一部分为画法几何：其中有制图基本知识，投影的基本知识，点、直线、平面的投影及它们之间的关系，投影变换，曲线、曲面及曲面立体的投影，截交线与相贯线，剖面图与断面图，标高投影，轴测投影等。

This paper studies and analyses the map projection transformation, using VC ++ programming language to realize three projection transformation: inclined position projection, Mercator projection and Gaussian M- Ke Lvge projection, and makes the application tests.

本文对地图投影变换做了尝试性的分析研究，利用VC++编程语言实现了斜轴等积方位投影、墨卡托投影和高斯-克吕格投影三种投影变换，并做了应用测试。

It respectively constructs quasi projection-separation facet sets of two convex polytopes while their orthogonal projection on the centerline overlap mutually. Afterward it judges the separation of two convex polytopes by confirming non-overlap in orthographic projection on the centerline or by finding out a projection-separation facet from two quasi projection-separation facet sets, otherwise a collision is judged.

该算法通过判断2个凸多面体在中心线上的正投影不相交，或者分别构造它们的准投影分离面集合，并从这2个集合中找到一个投影分离面，来判断2个凸多面体分离；否则，判断为相交。

In the optimal control of kinematics for redundant robots, two new concepts, the matrix weightability measure and the self-motion declinability measure are proposed. Further, a modified weighted gradient projection method which combines gradient projection method with weighted least-norm solution is presented, it can attain ideal optimal effects at low velocities.

本文对冗余自由度机器人的运动学、动力学和容错等方面的优化控制进行了深入的分析和探讨：在冗余度机器人运动学优化控制方面，提出矩阵可加权度和自运动可衰度的概念，将梯度投影法和加权最小范数解法有机的相结合，形成可优化能力强、关节速度较低的改进的加权梯度法。

Fist, comprehensive analysis on the current study on data processing is made, and characters of Newton methods about nonlinear surveying and mapping data processing are discussed, and then new solutions to parameters estimate with multi-sources, multi-types, multi-dimension, multi-precision bynonlinear least square are presented such as PSB algorithm, digital continuation and generalized digital continuation algorithm, cone model method, tensor analysis method, GCMA(mixed algorithm of gradient method and conjugate gradient method), combining algorithm based on Newton method and gradient method and confidence region and so on, and a new fast difference iterative algorithm is proposed towards parameters estimation containing random parameters in nonlinear models, and a new solutions to nonlinear least squares surveying and mapping adjustment by parameters estimation both considering the random and nonrandom parameters is presented after studying on nonlinear data processing in deformation monitoring, and at last primary analysis on error propagation of spatial data is made and approximate error propagation formula and error analysis formula to length and area are proposed.

首先比较全面分析了目前测量数据处理理论的研究现状，讨论了牛顿类方法在处理非线性模型参数估计方面的特点，研究并给出了求解多源、多类型、多维、多精度、非线性最小二乘测量平差参数估计的若干种新方法，这包括PSB算法、数值延拓及其广义数值延拓算法、锥模型法、张量分析法、基于最速下降法和牛顿法的组合算法、基于最速下降

This new method mainly comprises three steps: firstly, normalize the point-gradient vectors and calculate the block-gradient vectors and the corresponding block-coherence; then detect the noisy areas to eliminate the side effect of noise diffusing; finally, re-estimate all block- gradient vectors based on iteration and transform the gradient field to orientation field.

提出了一种基于梯度的健壮的指纹方向场估计算法，新算法首先归一化点梯度向量并计算块梯度向量及相应的块一致性；然后估计噪声区域；最后采用基于迭代的方法，重新估计所有块梯度向量并将梯度向量场转化为方向场。

This paper established a new kind of relation on projection——conic projection analogue by introducing the latitude circle and longitude circle analogues, then discussed the best choice of the conic vertex angle in this projection, and found the mathematical model and the applicable scope of this projection.

摘 要：本文通过引入类纬圈和类经圈，建立了一种新的投影关系——类圆锥投影，进而探讨了类圆锥投影中圆锥顶角的最佳选择，找到了类圆锥投影的数学模型和适用范围。

"Yes, now you can give yourself airs," she said, you have got what you wanted.

"对了，您现在高兴了，"她说道，这是您所期待的。

Then the LORD said to me: Rebel Israel is inwardly more just than traitorous Judah.

上主于是对我说：＂失节的以色列比失信的犹大，更显得正义。