Firstly , we simply introduce the scope , value and developement of the sparse quasi - newton method for unconstrained optimization problems 第一章为绪论简要介绍稀疏拟牛顿法的提出，研究情况及研究价值。
K was given by : k = ( x , g ) / ( g , g ] ( a . b ) denotes the usual inner product of the vectors a and b 于是我们在cane切、牛顿、拟牛顿等算法的基础上并受bar幻和borwein算法思想的启发，提出了稀疏拟牛顿法。
Techniques for ensuring the global convergence of the shamanskii modification of the newton method had not yet been studied since this iterative scheme was proposed 这种修正牛顿法自提出以来，其收敛性一直未被研究。但是最近， f
A new smoothing newton algorithm for sloving box constrained variational inequality is proposed by using chen - harker - kanzow - smale smoothing function 利用chen - harker - kanzow - smale光滑函数提出了一种解箱约束变分不等式的光滑牛顿法。
A smoothing function which can be approximated by ncp - function is given and the smoothing newton method is applied to resolve this nonsmooth operator equation 构造一个光滑化函数逼近ncp -函数，利用光滑化牛顿法求解此非光滑算子方程。
Furthermore , the global and superlinear convergence of the shamanskii modification of the newton method with the new line search are proved under the weaker conditions than those in ref [ 10 ] ( i . e . , 在本章中，我什1将邪a ？ nans汕6修正牛顿法的迭代形式作了进一步的改进，改进后的sha 。 a 。
Tests on a practical radial distribution system have shown that , the proposed method is as robust as , but more efficient than the back / forward sweep method 文中以一个实际的中等规模配电系统为例，分析、比较前推回推法、导出的近似牛顿法、经典牛顿法等的收敛性和计算速度，证实上述研究结论。
So , this method has cured the chronic disease - - the problem of the convergence being difficult when newton method is used to solve the ehl problems under the conditions of the high speed and heavy load 从而解决了牛顿法在求解高速、重载条件下弹流问题时收敛困难的顽症，这是本文的主要成果之一。
On the basis of this reformulation , it is proved that the system of nonsmooth equations is strongly semismooth so that the generalized newton method for solving this system possesses locally quadratic convergence 在此基础上，证明了非光滑方程是强半光滑的，因而解此方程的广义牛顿法具有局部二次收敛性。
These techniques can be implemented with relatively little computational overhead and lead to a large reduction in the number of subintervals that must be tested during the interval newton procedure 综上所述，以上两种改进方法都能大大地减少区间牛顿法的迭代次数和计算时间，提高了算法的有效性和高效性。
