收敛性

Using the resolvent operator technique, we establish the equivalence between the generalized set-valued quasi variational inclusions in Banach spaces and the fixed point problems, and some perturbed iterative algorithms, prove that its proximate solution converges to its exact solution in real Banach spaces.

利用这种等价性，建立了一些摄动迭代算法，并证明了近似解序列强收敛于精确解。

In Chapter 3 Firstly, the exponential stability in mean square and almost sure exponential stability for neutral stochstic neural networks with time-varying delay can be discussed by using the linear matrix inequality and the semimartingale convergence theorem; And our sufficient conditions are less conserative; Secondly, by utilizing the fixed point theorem, some sufficient and necessary conditions ensuring the asymp- totic stability in mean square for neutral stochastic neural networks with time-varying delays can be given.

第三章首先，利用线性矩阵不等式方法和半鞅收敛定理，考虑了一类具变时滞中立型随机神经网络的二阶矩指数稳定性和几乎必然指数稳定性，所得到的条件保守性要好；其次，采用不动点方法，给出了具变时滞中立型随机神经网络的二阶矩渐近稳定性的充要条件。

Neutral equation; stochastic functional differential equation; stochastic differential equation with delay; infinite delay; asymptotic propertie; semimartingale convergence theorem; Markovian switching; moment stability; moment boundedness

基础科学，数学，概率论、数理统计中立型方程；随机泛函微分方程；随机延迟微分方程；无限时滞；渐近性质；半鞅收敛定理； Markov调制；矩稳定性；矩有界性

There are simple rules and quick convergence speed for SDPS.

该方法给出的适配粒子群算法规则简单、收敛速度快，得到的解集有较好的分散性和均匀性。

Compared with IEKCA, GKPSOKCA needs less parameters to determine, can be easily implemented, and has stable convergence characteristic with good computational efficiency.

粒子群K均值聚类算法需要调整的参数少，易于实现，计算速度快，且具有稳定的收敛特征，能很好满足群控系统实时性的要求。

We study the attractive manifold method of the iterative learning control for a class of degenerate systems in the chapter Ⅲ. When the learning control systems don't satisfy the convergence condition, we present the learning control method satisfying the condition by constructing a stable and attractive manifold corresponding system. This method makes the system with better robustness.

第三章主要研究了一类退化系统目标跟踪的迭代学习控制的吸引流形方法，在系统不满足一般收敛条件的情况下，我们通过构造一个相应于所给系统稳定而吸引的流形，导出所满足要求的迭代学习控制，该方法对系统有较好的鲁棒性。

The mixed method raise the convergent rate of the conjugate gradient method, and solve the problem which the steepest descent method can not solve in the condition with badly characteristics for the objective function.

混合算法既提高了共轭梯度算法的收敛速度，又解决了目标函数"性态不优"时，最速下降法难以求解的问题。

Thirdly, under the condition with noαpriori smoothness, in order to obtain the optimal convergence rates, it is not practical to use theαpriori rule. And it is necessary to use the a posteriori stopping rule which not only depends on the error boundδbut also on the perturbed data y~δ.

再次，在没有先验的光滑性信息情况下，为了获得最优收敛速率，利用先验选取准则则变得不再实用，而利用不仅依赖于误差界δ而且依赖于扰动数据y~δ的后验停止准则是必要的。

It is proved by the theoretical analysis and simulation result that the method can avoid the complicated mathematical analysis of the object and has the features such as fast convergence and strong robustness

理论分析与仿真结果表明，该算法可避免对受控对象做复杂的数学分析，具有收敛速度快，鲁棒性较强的特点。

Stochastic convex programming; Monte Carlo methods; Financial optimization; Convergence with probability one; Optimality condition; Monte Carlo penalty function methods; Nonsmooth optimization; Directional derivative; Subdifferential; Confident interval; Conditional Value-at-Risk; Optimal reinsurance

基础科学，数学，运筹学随机凸规划； Monte Carlo方法；金融优化；以概率1收敛；最优性条件； Monte Carlo罚函数法；非光滑优化；方向导数；次微分；置信区间；条件风险价值；最优再保险

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。