A class of strong convergence theorem for an arbitrarily adapted stochastic sequence without the non - decrease condition was established by using the truncation method of stochastic variables and the stop time 摘要引入了随机变量的截尾和停时的概念，在定理条件及其证明过程中适当地定义随机变量的截尾和停时，并通过定义鞅差序列和利用鞅差序列的收敛定理，得到了一类关于任意随机适应序列的强收敛定理。
For both methods , at most two reduced linear systems of equations with the same coefficient matrix need to be solved in order to get iterative directions at each iteration and the iterative matrix involves only constraints in the working set , whose cardinality are much less than the number of original constraints 在其每次迭论文摘要代中，只有有效工作集中的约束参与计算。在本文中，我们在facchinei一fischer一kanzowkkt点有效约束集识别技术的基础上提出了三个具有强收敛性的qp一free算法。
A kind of complete convergence of sums for negatively associated sequences of non - identically distributed random variables , in the second chapter , is obtained and the requirement of known results are weakened to the condition that absoluted moment - larger than zero - is finite . the strong convergence of negatively associated sequences of non - identically distributed random variables is discussed in the third chapter . in the fourth chapter , after extend the laws of the iterated logarithm of strong stationary case to weak stationary case , we obtain the strong convergence rate for negatively associated sequences of non - identically distributed random variables in linear models 其中第二章讨论了一类不同分布的na列的加权和的完全收敛性，我们把已有的结果对矩的要求放宽到了只要求大于0的绝对矩有限的情形；第三章讨论了不同分布的na列的加权和的强收敛性；第四章首先把文[ 10 ]的关于na的重对数律由强平稳的情形推广到了弱平稳不同分布的情形，然后得到了线性模型中不同分布的na误差列的收敛速度。
Because three systems of equations solved at each iteration have the same coefficients , so the ammount of computation are less than that of the existing sqp algorithms . under some common conditions ( such as the second order sufficient condition ) which are used in some references , we prove that the algorithm possesses not only global convergence , but also strong convergence and superlinear convergence 该算法在每次迭代时所需解的三个线性方程组具有相同的系数，因此计算量要比现有的sqp方法有所减少；在与一些文献平行的假设条件(如二阶充分条件)下，论文证明了算法不仅具有全局收敛性，而且还具有强收敛性和超线性收敛性
