梯度法

The definition of generalized conjugate (or M-conjugate) is introduced and the generalized conjugate gradient method is presented.

引入了广义共轭的概念，在此基础上提出了广义共轭梯度法。

Based on the genetic algorithm and the method of conjugate gradient, a method for optimizing the model parameters is developed.

基于遗传算法和共轭梯度法确定最优化模型参数，利用该模型拟合了2种硫化胶的应力松弛系数和永久变形率随时间变化的数据。

Now, the rapid development of computer and occurrence of a great deal of large-scale optimization problems make the researches in conjugate gradient method revive.

近年来，随着计算机的飞速发展和实际问题中大规模优化问题的涌现，寻找快速有效的共轭梯度法成为了学者们研究的热门方向之一。

Some methods are direct in principle but are usually used as though they were not, e.g. GMRES and the conjugate gradient method .

有些方法是直接在原则上，但通常用作但他们没有，例如： GMRES方法和共轭梯度法。

According to the filter matrix particularity, the filter equation was solved by using conjugate gradient method.

并根据滤波矩阵的特殊性，釆用共轭梯度法求解滤波方程。

In this dissertation, we presented the global convergence properties of nonlinear conjugate gradient methods without line search and with strong Wolfe conditions, Goldstein inexact line search.

本文给出了无约束最优化算法—非线性共轭梯度法在不需线搜索和用强Wolfe条件下以及用Goldstein非精确线搜索产生搜索步长情况下的全局收敛性证明。

Nonlinear Conjugate Gradient Method; Line Search; Sufficient Descent Direction; Global Convergence

基础科学，数学，运筹学非线性共轭梯度法；线性搜索；充分下降方向；全局收敛性

In the first section, we introduce the development of the conjugate gradient methods.

在第一部分中我们介绍了共轭梯度法的发展过程及其研究现状。

In comparison with classic conjugate gradient methods, the decrease of objective function is contained in the two new methods.

与经典的共轭梯度法的区别是新方法中体现了函数值下降量的信息。

Keywords Closed convex cone;gradient projection method;Least-squares solution;Inverse matrix problem;Inverse eigenvalue problem;Matrix completion problem;Optimal approximation

Article From 湖南大学；应用数学博士论文 2005年度闭凸锥；投影梯度法；最小二乘解；矩阵反问题；矩阵逆特征值问题；矩阵完全化；最佳逼近

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。