查询词典 projection gradient method

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In this paper, a series of lunar map projection formulas are deduced including azimuthal projections, cylindrical projections and conical projections. The lunar map projections software is compiled. By caculating lunar map projection distortions, their projection distortion rules are found. Base on the lunar exploration mission, the lunar map projection scheme is given in this paper. The azimuthal conformal projection or the circumcenter perspective azimuthal projection is usually used in small areas, especially in two poles. When the whole map of the moon is needed, the azimuthal conformal projection or the circumcenter perspective azimuthal projection is used within 10° in the poles, and the traverse tangent cylindrical conformal projection or the normal secant conical conformal projection can be used in else areas, furthermore, band-division is necessary to reduce the projection distortion.

本文推导了基于月球参考球的各种投影公式，主要包括方位投影、圆柱投影和圆锥投影；编制了月球地图投影计算软件；对多种月球的投影变形进行了详细的计算，总结分析了各种月球投影的变形规律；结合月球探测的需要，给出了月球投影方案的建议：对于局部的面积较小的投影区域，建议使用等角方位投影或外心透视方位投影；如果绘制月面全图，在两极10°范围内采用等角方位投影或外心透视方位投影，其余区域可以采用等角横切圆柱投影和等角正割圆锥投影，并且要进行分带处理。

Furthermore, the first-order optimality condition and its equivalent reformulations for generalized semi-infinite max-min programming with a non-compact set are presented using the lower-Hadamard directional derivative and subdifferential.2. Chapter 3 studies the gradient-type methods for unconstrained optimization problems. Section 1 proposes a new class of three-term memory gradient methods. The global convergence property of the method is established. Furthermore, in order to improve the convergence property of the method, a new class of memory gradient projection methods is presented with the property that the whole sequence of iterates converges to a solution to the problem under the conditions such as pseudo-convexity and continuous differentiability of objective function. In section 2, two new classes of methods, called gradient-type method with perturbations and hybrid projection method with perturbations, are proposed. In these methods, non-monotone line search technique is employed, which makes them easily executed in computer.

第3章研究了无约束优化问题的梯度型算法，第1节提出了一类新的三项记忆梯度算法，讨论了算法的全局收敛性，进一步提出了一类新的具有更好收敛性质的记忆梯度投影算法，并证明了该算法在函数伪凸的情况下具有整体收敛性，第2节在非单调步长搜索下提出了带扰动项的梯度型算法及其混合投影算法，这两类算法的一个重要特征就是步长采用线搜索确定而不象许多文献中那样要求步长趋于零，这样更容易在计算机上实现，在较弱的条件下证明了这些算法的全局收敛性，数值算例表明了算法的有效性。

Among used machine learning methods, the gradient descent method is widely used to train various classifiers, such as Back-propagation neural network and linear text classifier. However, the gradient descent method is easily trapped into a local minimum and slowly converges. Thus, this study presents a gradient forecasting search method based on prediction methods to enhance the performance of the gradient descent method in order to develop a more efficient and precise machine learning method for Web mining.However, a prediction method with few sample data items and precise forecasting ability is a key issue to the gradient forecasting search method. Applying statistic-based prediction methods to implement GFSM is unsuitable because they require a large number of data items to model a prediction model. In the contrast with statistic-based prediction methods, GM(1,1) grey prediction model does not need a large number of data items to build a prediction model, and it has low computational load. However, the original GM(1,1) grey prediction model uses a mathematical hypothesis and approximation to transform a continuous differential equation into a discrete difference equation in order to model a forecasting model.

其中梯度法是一个最常被使用来实现机器学习的方法之一，然而梯度法具有学习速度慢以及容易陷入局部最佳解的缺点，因此，本研究提出一个梯度预测搜寻法则(gradient forecasting search method， GFSM)来改善传统梯度法的缺点，用来提升一些以梯度学习法则为基础的分类器在资讯探勘上的效率与正确性；而一个所需资料量少、计算复杂度低且精确的预测模型是梯度预测搜寻法能否有效进行最佳解搜寻之关键因素，传统统计为基础之预测方法的缺点是需要较大量的数据进行预测，因此计算复杂度高，灰色预测模型具有建模资料少且计算复杂度低等优点，然而灰色预测理论以连续之微分方程式为基础，并且透过一些数学上的假设与近似，将连续之微分方程式转换成离散之差分方程式来对离散型资料进行建模及预测，这样的作法不尽合理，且缺乏数学理论上的完备性，因为在转换过程中已经造成建模上的误差，且建模过程仅考虑相邻的两个资料点关系，无法正确反应数列未来的变化趋势。

In chapter 2 we propose a linear equality constraint optimization question , the new algorithm is combined with the new conjugate gradient method(HS-DY conjugate gradient method)and Rosen"s gradient projection method , and has proven it"s convergence under the Wolfe line search.In chapter 3 we have combined a descent algorithm of constraint question with Rosen"s gradient projection, and proposed a linear equality constraint optimization question"s new algorithm, and proposed a combining algorithm about this algorithm, then we have proven their convergence under the Wolfe line search, and has performed the numerical experimentation.

在第三章中我们将无约束问题的一类下降算法与Rosen投影梯度法相结合，将其推广到线性等式约束最优化问题，提出了线性等式约束最优化问题的一类投影下降算法，并提出了基于这类算法的混合算法，在Wolfe线搜索下证明了这两类算法的收敛性，并通过数值试验验证了算法的有效性。

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。

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。

The first conductivity base board comprises: a base material, a first projection, a second projection and a light spacer; the first projection and the second projection are installed on the base material with central line symmetry, the second projection is the image structure of the first projection relative to the central line.

第一导电基板包括一底材、一第一凸块、一第二凸块及一光间隔物，第一凸块及第二凸块以对称于一中心线的方式设置于底材之上，第二凸块为第一凸块对应于此中心线的镜射结构。

In Salsola passerina -Reaumuria soongorica community, the first ordination axes explains the salinization gradient, along the order of Caragana tibetica community,Salsola passerina-Oxytropis aciphylla community,and Reaumuria soongorica-Salsola passerine community,soil alkalization increases. The second ordination axis explains soil structure gradient, along the order of Caragana tibetica community, Reaumuria soongorica-Salsola passerina community and Salsola passerina community, soil texture becomes coarser. In the Stipa breviflora-Stipa grandis community, the first ordination axis indicates the soil water gradient, and the second ordination axes explains hydrothermal coupling gradient. In the Prunus mongolica-Ulmus glaucescens community, the first ordination axis explains the soil pH gradient, along the order of Ulmus glaucescens-Prunus mongolica community, Prunus mongolica-Potentilla fruticosa community, and Potentilla fruticosa-Prunus mongolica community, soil pH value reduces. The second ordination axis explains soil structure gradient, along the order Prunus mongolica-Ulmus glaucescens community, and Prunus mongolica-Potentilla fruticosa community, the contents of silt and clay increase, and soil texture suggests a fine trend.

在珍珠猪毛菜-红砂群落，第一排序轴反映了土壤盐碱化梯度，沿着藏锦鸡儿群落—珍珠猪毛菜、猫头刺群落—珍珠猪毛菜、红砂群落序列，土壤盐碱化程度不断增强；第二排序轴则反映了土壤结构梯度，沿着藏锦鸡儿群落—珍珠猪毛菜、红砂群落—珍珠猪毛菜、猫头刺群落序列，土壤质地逐渐粗化；在短花针茅-大针茅群落，第一排序轴反映了土壤水分梯度，第二排序轴反映了海拔梯度上的水热组合梯度；在蒙古扁桃-灰榆群落，第一排序轴反映了土壤pH梯度，沿着灰榆、蒙古扁桃群落—蒙古扁桃、金露梅群落—蒙古扁桃群落序列，土壤pH值逐渐下降；第二排序轴主要反映了土壤结构梯度，沿着蒙古扁桃群落—灰榆、蒙古扁桃群落—蒙古扁桃、金露梅群落序列，土壤中粉粒、粘粒含量逐渐增加，土壤质地呈细化趋势。

In Salsola passerina-Reaumuria soongoriea community, the first ordination axes explains the salinization gradient. along the order of Caragana tibetica community, Salsola passerina-Oxytropis aciphylla community, and Reaumuria soongorica-Salsola passerine community, soil alkalization increases. The second ordination axis explains soil structure gradient, along the order of Caragana tibetica community, Reaumuria soongorica-Salsola passerina community and Salsola passerina community, soil texture becomes coarser. In the Stipa breviflora-Stipa grandis community, the first ordination axis indicates the soil water gradient, and the second ordination axes explains hydrothermal coupling gradient. In the Prunus mongolica-Ulmus glaucescens community, the first ordination axis explains the soil pH gradient, along the order of Ulmus glaucescens-Pnuius mongolica community, Prunus mongolica-Potentilla fruticosa community, and Potentilla fnuicosa-Prunus mongolica community, soil pH value reduces. The second ordination axis explains soil structure gradient, along the order Prunus mongolica-Ulmus glaucescens community, and Prunus mongolica-Potentilla fruticosa community, the contents of silt and clay increase, and soil texture suggests a fine trend.

在珍珠猪毛菜－红砂群落，第一排序轴反映了土壤盐碱化梯度，沿着藏锦鸡儿群落－珍珠猪毛菜、猫头刺群落－珍珠猪毛菜、红砂群落序列，土壤盐碱化程度不断增强；第二排序轴则反映了土壤结构梯度，沿着藏锦鸡儿群落－珍珠猪毛菜、红砂群落－珍珠猪毛菜、猫头刺群落序列，土壤质地逐渐粗化；在短花针茅－大针茅群落，第一排序轴反映了土壤水分梯度，第二排序轴反映了海拔梯度上的水热组合梯度；在蒙古扁桃－灰榆群落，第一排序轴反映了土壤pH梯度，沿着灰榆、蒙古扁桃群落－蒙古扁桃、金露梅群落－蒙古扁桃群落序列，土壤pH值逐渐下降；第二排序轴主要反映了土壤结构梯度，沿着蒙古扁桃群落－灰榆、蒙古扁桃群落－蒙古扁桃、金露梅群落序列，土壤中粉粒、粘粒含量逐渐增加，土壤质地呈细化趋势。

When this condition occurs, inbound replication with the source partner is stopped on the destination domain controller and event ID 2042 is logged in the Directory Services event log.

计算机密码学是研究计算机信息加密、解密及其变换的科学，是数学和计算机的交义学科，也是一门新兴的学科。

Instructions: click on the thumbnails to see a larger image, then use the left-right arrow keys to scroll through the slideshow.

使用说明：滑鼠点在小图上即可放大观赏。开启后键盘左右键可用来换照片。