收敛性

According to stochastic approximation theory, when deterministic continuous time method is used to analyze convergence of MCA learning algorithms, the learning rate is required to approach to zero.

具有固定学习速度的MCA学习算法的收敛性分析根据随机逼近理论，当确定连续时间方法被用于分析MCA学习算法的收敛性时，学习速度被要求趋于零。

Moreover, we give some dual properties of these problems, and on this basis, we present a dual algorithm for solving the nonconvex conic model trust-region subproblem.

论文分析了这些问题的对偶性质，在此基础上，通过对偶提出了求解锥模型信赖域子问题的算法，同时证明了算法的全局收敛性以及局部Q-超线性收敛性，并给出了一些数值算例以说明算法的有效性。

Under mild conditions, we prove the global and superlinear convergence of the method.

在较弱的条件下，得到了算法的全局收敛性及其超线性收敛性。

Under mild conditions, we establish the global and superlinear convergence results for the method.

在适当的假设条件下，我们证明了算法具有全局收敛性和超线性收敛性。

The method proves to have superlinear convergence rate under some mild conditions.

给出的算法是可实现的并具有全局收敛性，且在适当假设下具有超线性收敛性。

By the way, we describe the modified quasi-Newton algorithm used the line search , and have given its global convergence and superlinear convergence.

接下来描述了采用线性搜索的修正拟Newton算法，并给出了它的全局收敛性与超线性收敛性。

Furthermore, the global convergence and superlinear convergence rate are proved under mild assumptions without the strict complementarity.

此外，在不需要严格互补的温和条件下，我们证明了算法的全局收敛性和超线性收敛性。

By choosing the proper parameters, we can prove that the new method has global and superlinear convergence properties under suitable conditions.

通过选择适当的参数，证明了改进的BFGS方法对于一类更广的搜索准则保持局部收敛性，在Wolfe搜索准则下方法还具有超线性收敛性。

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。

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。