收敛性

We prove that the economic growth mode will be nonlinear in a region restricted by Minimum Government Scale, conditional convergence and club convergence would be found and the regional gap would reduce the first, then enlarge and reduce in the last.

我们证明，存在最小政府规模的经济其增长是非线性的，经济收敛性在短期表现为条件收敛与俱乐部收敛的双重特征，并且地区差距的变化将呈现出缩小-扩大-再缩小的动态特征。

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。

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。

In order to make the new recursive method convergence fast, the RLS-like forgetting factor is introduced to construct the new data Hankel matrices. In the framework of subspace methods, the gradient type subspace tracking method is used to implement the update of the state subspace, which results the unbiased estimate. Different from traditional offline method, the system matrices are recursively computed using RLS method. The convergence analysis of the proposed method is given and finally, the efficiency of this method is illustrated with a simulation example.A new closed-loop identification method is proposed to implement consistency estimation of closed-loop subspace identification.

引入RLS-like遗忘因子机制构造新的数据矩阵，更好地跟踪系统时变信息，提高递推算法的收敛速度；在子空间辨识框架内，采用梯度型子空间跟踪算法实现对状态子空间的更新，避免了子空间近似带来的估计有偏性；与传统的离线算法不同，在得到系统状态子空间后，基于递推最小二乘方法提出新的算法，实现对系统矩阵的递推估计；并给出递推子空间辨识算法的收敛性分析；最后通过仿真实例验证算法的有效性。

Inspired by these results, in this paper, we first give the definition of a new mapping ? uniformly Lipschitz asymptotically nonexpansive mapping on a compact subset of a uniform convex Banach space, then construct three-step iterative sequences of uniformly Lipschitz asymptotically nonexpansive mapping in this subset . We proved the convergence of this three-step iterative sequences for uniformly Lipschitz asymptoticallynonexpansive mapping, Further more, we proved this three-step iterative sequences with an error member converge to fixed points.

从中得到启发，在本文我们首先定义了一致凸Banach空间某非空紧子集上的一种新的映射——一致李普希兹渐进非扩张映射，在该紧子集上构造关于一致李普希兹渐进非扩张映射的三步迭代序列以及具误差的三步迭代序列，先来讨论三步迭代序列的收敛性，进而讨论具误差的三步迭代序列的收敛性。

Firstly, an empirical approximation model of stochastic programming is obtained by replacing the probability measure of original program with empirical probability measure. Sequentially, the constrained stochastic programming is transformed into an equivalent unconstrained stochastic programming. Finally, using the epi-convergence theory, the almost everywhere upper semiconvergence of optimal solution set of empirical approximations for stochastic programming is obtained.

首先通过经验概率测度替代初始规划的概率测度得到随机规划的经验逼近模型，然后将带有约束的随机规划问题转化成与其等价的无约束的随机规划问题，最后利用上图收敛性理论，给出了随机规划经验逼近最优解集的几乎处处上半收敛性。

And trust region type algorithm with memoryless technology not only satisfies new factorized quasi-Newton equation, but also saves much storage and algebraic operations than the original factorized quasi-Newton methods.we prove it posses the global convergence and the local superlinear convergence under some condition.

本文中利用无记忆技术产生的无记忆型信赖域算法不仅满足新分解牛顿方程，具有其所有的良好性质，而且比一般的分裂拟牛顿法节省存储空间，减少计算量。本文证明了在一定假设条件下该算法具有全局收敛性及局部超线性收敛性。

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。