牛顿性

The Newton law , law of universal gravitation , Coulomb's law , law of increase of entropy wait, all with whose elegance , general suitable and concordance give beautiful being shocked to person.

牛顿定律，万有引力定律，库仑定律，，熵增加原理等，都以其简洁性，普适性与和谐性给人以美的震撼。

In Chapter 4, using the formula A_k(2) given by Wei, we propose a new A_k(2)-SQP method, which develepments the using of the quasi-Newton formula BFGS, and combines with SQP method to solve constrained optimization problems, the corresponding algorithm possesses global convergence and supei linear convergence property.

第四章，利用韦提出的A_κ(2)公式，我们给出了一种A_κ(2)-SQP方法，该方法把拟牛顿修正公式BFGS进行了推广，并结合SQP方法去解约束优化问题，相应的算法具有全局收敛性和超线性收敛性。

For the original infinite dimensional problem, if the inexact quasi-newton method with Broyden updating can not converge quickly , for example, it can not attain super linear convergence rate , then when the discretization is becoming finer and finer , we can not get fast convergence rate for the corresponding finite dimensional problem.

对于原来的无限维问题，如果使用不精确Broyden方法不能得到较快的收敛速度，比如超线性收敛性，那么当离散化逐渐加细的时候，对于所得的有限维问题使用不精确Broyden方法也不可能得到较快的收敛速度，所以有必要在无穷维空间上对收敛性问题加以分析，从而为不精确拟牛顿法结合投影法求解算子方程做好准备。

Global and local superlinear/quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs.

基于此给出了求解箱约束变分不等式的一种阻尼牛顿算法，在较弱的条件下，证明了算法的全局收敛性和局部超线性收敛率，以及对线性箱约束变分不等式的有限步收敛性。

A damped Newton type method was presented based on it.Global and local superlinear/quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs.

基于此给出了求解箱约束变分不等式的一种阻尼牛顿算法，在较弱的条件下，证明了算法的全局收敛性和局部超线性收敛率，以及对线性箱约束变分不等式的有限步收敛性。

In chapter II,the preliminary knowledgefor accomplishing this research is presented,and the well-posed problem ofthe thin-plate flow of non-Newtonian viscous fluids is testified.By using themonotone operator theory and Schauder's fixed point theorem,the generalizedsolution's existence and uniqueness theorem for the thin-plate flow problem ofnon-Newtonian viscous fluids is obtained under reasonable conditions.

第二章给出了进行本项研究所需的一些预备知识，对非牛顿粘性流体薄板流问题广义解的适定性进行了研究，应用单调算子理论和不动点定理，在合理的条件下，证明了非牛顿粘性流体薄板流问题广义解的存在性，唯一性定理。

In the first chapter, the application background and the main algorithms of the complementarity problems is introduced. In Chapter 2, some basic definitions and theories of complementarity problems are introduced. The 3rd chapter is the most important part of this paper, in which a new class of smoothing Newton method is detailed, also the global and local superlinear convergence is established for the method. In the 4th chapter, we propose some numerical experiment, and the results show the effectiveness of the proposed algorithms.

全文共分为四章，各部分内容安排如下：第一章是绪论部分，介绍了互补问题的应用背景和近年来有关互补问题求解方法的研究成果；第二章介绍了与互补问题相关的一些定义以及相关的定理和推论；第三章是本文的重点，构造了求解互补问题的一类光滑牛顿法，从理论上证明了算法的全局收敛性和局部超线性收敛性；第四章是数值实验，通过数值试验的结果进一步证明了算法的可行性和有效性。

To solve it, we turn it into nonsmooth equations, utilizing inexact theory we give an inexact generalized Newtons method and under some mild conditions we prove that it is global convergence and superlinear convergence .

首先将其约束问题的求解转化为非光滑方程组的求解，然后利用不完全求解理论给出了一个非精确的广义牛顿算法，在一定的条件下证明了算法的全局收敛性和局部超线性收敛性并给出了LC~1非线性约束问题的收敛性条件。

A class of modified BFGS algorithm which satisfies the new quasi-Newton equation is proposed in the paper[1],and the global convergence of the algorithm is proved under the condition that the objective function is uniformly convex.

文献[1]曾在已建立的一类新拟牛顿方程 Bk+1sk=yk-=yk+kγskTsksk的基础上，证明了满足新拟牛顿方程的一类改进BFGS算法在目标函数为一致凸的条件下，具有全局收敛性。

In Chapter Six,we translate the equation of the iterative step of nonsmooth Newton-type method for nonlinear SDP into the conversional linear equations by the tensor technique. By using the equivalency conditions in Chapter Five, we establish the local convergence of this method.

在第六章中，我们通过张量技术把非线性半定规划问题的非光滑牛顿型法迭代步方程转化为一般的线性方程组，并利用第五章中的等价性结论分析了这种方法的局部二次收敛性。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。