收敛

Under mild conditions,a new feasible descent algorithm is presented and its global and superlinear convergence are proved by using the technique of combining generalized projection method with sequential systems of linear equations.

在较温和的条件下，采用广义投影和序列线性方程组相结合的技术，建立一个新的可行下降算法，证明了算法的全局收敛性和超线性收敛性。

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。

In this paper, we mainlydiscuss the above functions and apply the violation constrained functions to filterSQP methods the algorithms, furthermore, we prove that the new algorithms haveglobal convergence and superlinear convergence under the mild conditions.

本文着重讨论这几种NCP类函数的性质，并把它们所定义的违反约束度函数应用于SQP算法中，并证明了在一定的条件下新的算法具有全局收敛性和超线性收敛性。

Since a new generalized projection technique is contained in the auxiliary direction formula, under some mild assumptions without the strict complementarity, the global convergence and superlinear convergence of the algorithm can be obtained.

由于一种新的广义投影技术包含在辅助方向的计算公式中，因而在无严格互补等较温和的假设下便可得到算法的全局收敛性及超线性收敛性。

LC1 unconstrained optimization problem was discussed in the second chapter, giving a new trust region method and proving its global convergence and superlinear convergence under some mild conditions .

第二章讨论了LC~1无约束优化问题。给出了一个新的信赖域算法，并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。

In Chapter 2, combining two types of the preconvex part of modified Broydens family with Armijo line search, we get two algorithms for solving unconstrained optimization problems, and prove these algorithms are global and superlinear convergence under some suitable conditions.

第二章，将两种修改Broyden非凸族与Armijo线搜索相结合，得到了求解无约束最优化问题两种算法，在适当的条件下，证明了这些算法具有全局收敛性和超线性收敛性。

In Chapter 3, we propose two new quasi-Newton type trust region methods for solving unconstrained optimization problems. These algorithms combine two types of the preconvex part of modified Broydens family proposed in chapter 1 with trust region algorithm effectively, they have global convergence property and superlinear convergence rate.

第三章，给出了用来求解无约束最优化问题两种新的拟牛顿信赖域算法，这些算法将第一章给出的两种修改Broyden非凸族与信赖域算法有效结合起来，它们具有全局收敛性和超线性收敛速度。

Which possesses global convergence and locally superlinear convergence proven without strict complementarity at the Danskin point.

在不假设在Danskin点处满足严格互补条件的情况下证明了算法具有超线性收敛速度及全局收敛的性质。

After summarizing the waveform relaxation methods and domain decomposition, we finish some research on optimal Schwarz waveform relaxation algorithm as follows: In the first part, we apply Schwarz waveform relaxation methods on telegraph equation system to get optimal transmission conditions to speed up the algorithm.

在对波形松弛算法以及区域分解进行了综述性介绍后，本文对Schwarz波形松弛迭代算法具体进行了以下研究：首先，本文将在电报方程系统上应用Schwarz波形松弛迭代算法，通过强制加入新的局部传输条件分别给出了两种加速算法并通过定理保证了其优化后的收敛性，进而得到优化Schwarz波形松弛算法，然后通过数值试验对传统Schwarz波形松弛算法与优化Schwarz波形松弛算法进行了比较，研究了收敛率与优化系数的关系，找到了使算法最优的系数取值；最后得出优化后的Schwarz波形松弛算法优于常规Schwarz波形松弛算法的结论。

On the basis of the advantages of the previous distillation calculation algorithms, by eliminating the non—zero elements to the two sides of the tridiagonal band of elements in the component material balance equations by correlation of the draw rate from the main column to the sidestrippers and the return vapor stream from the sidestrippers to the main column, it changes these equations into a typical form of the tridiagonal matrix, and uses the simultaneous convergent strategy of the main column and the side strippers to speed the algorithm convergent rate.

在吸收前人蒸馏计算算法优点的基础上，通过求解主塔抽出到汽提塔的量和汽提塔返回主塔的蒸汽流之间的关联，以便消除组分物料平衡方程组系数阵中的三对角线两边的非零元素，使它转化为典型的三对角矩阵形式，而且使用主塔和汽提塔同时收敛策略，加快了算法收敛速度。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。