查询词典 gradient method

FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

Combined CD method and a new conjugate gradient method given by Liu.Y, Storey. C, the second class of nonlinear conjugate gradient method is proposed, which not only has descent property, but also is proved global convergence with the general Wolfe line search. Finally, the numerical results show this class of conjugate gradient methods is very efficient.

第二类算法是结合CD法和Liu.Y， Storey.C提出的新共轭梯度法，提出一类新的非线性共轭梯度法，新方法不但具有下降性质，而且在推广的Wolfe线搜索下是全局收敛的，最后进行了数值验证。

Chapter 1 is the introduction, which introduces conjugate gradient method, gradient-related memory method and the main results obtained in t...

第一章是本文的绪论部分，简要介绍了记忆梯度方法和共轭梯度方法的发展现状以及本文的主要工作。

Meanwhile the biconjugate gradient method instead of the conjugate gradient method is used to accelerate the iteration process.

同时用双共轭梯度法代替共轭梯度法来加速迭代过程。

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。

The choice of step-length strongly affects the convergence rate of the Gradient Method, the classical Gradient Method—the method of steepest descent converges rather slowly in most cases, the poor behavior of the method is due to the optimal choice of step-length.

步长的选取对梯度法的收敛速度影响非常大，经典的梯度法-最速下降法在大多数情况下收敛得相当慢的原因在于最优步长的选取。

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。

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

Model comparisons for estimating water and heat fluxes of reed wetland ecosystem in Panjin were done among Profile gradient method,Bowen ratio energy balance method and Eddy covariance method,based on the data from July 1 to July 31,2005 by open-path eddy covariance system(Li-7500,Li-cor Inc,USA) and the micro-climate gradient observation system.

利用2005年7月盘锦芦苇湿地生长旺季的小气候梯度系统30 min观测资料和开放式涡动相关系统10Hz原始观测资料，比较并分析了廓线法、波文比能量平衡法与涡动相关法计算的芦苇湿地生态系统水热通量。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。