具有大步长邻近点的对称交替方向法的收敛性研究

发布时间：2018-02-15 08:22

  本文关键词： 凸规划 对称交替方向法 邻近点 大步长　出处：《南京大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文研究具有大步长邻近点的对称交替方向法的收敛性与取较大步长因子时算法的数值表现。对称交替方向法在一次迭代中,更新对偶变量λ两次,故交替方向法可以视为对称交替方向法的特例。在迭代中,更新对偶变量的计算量小,而求解x,y子问题的计算量大。所以如果能通过增加对偶变量的更新次数来减少求解x,y子问题的次数,那么很有可能可以提升算法的效率。鉴于经典的对称交替方向法在求解具有两个算子的可分凸规划问题上数值表现优越,但其收敛性在理论上没有保证,所以我们通过引入步长因子来考虑带步长因子的对称交替方向法的收敛性分析。此前,何老师等通过引入步长因子,考虑了对称交替方向法的收敛性。本文在此基础上,将对称交替方向法的步长因子范围扩大。我们证明了在该范围内对称交替方向法的全局收敛性。此外,为了使算法更加灵活,我们在子问题中引入了邻近项。更多的交替方向法型算法可以被视为对称交替方向法的特例。并通过实验说明了带较大步长因子的对称交替方向法的数值有效性。
[Abstract]:In this paper, the convergence of symmetric alternating direction method with large step size adjacent points and the numerical performance of the algorithm with large step size factor are studied. In one iteration, the symmetric alternating direction method updates the dual variable 位 twice. Therefore, the alternating direction method can be regarded as a special case of the symmetric alternating direction method. Therefore, if we can reduce the number of times to solve xy subproblem by increasing the number of updates of dual variables, It is possible to improve the efficiency of the algorithm. Whereas the classical symmetric alternating direction method is superior in solving separable convex programming problems with two operators, its convergence is not guaranteed in theory. So we consider the convergence analysis of symmetric alternating direction method with step size factor by introducing step size factor. Previously, he et al. considered the convergence of symmetric alternating direction method by introducing step size factor. The step size factor range of symmetric alternating direction method is expanded. We prove the global convergence of symmetric alternating direction method in this range. In addition, in order to make the algorithm more flexible, We introduce the adjacent term into the subproblem. More alternative direction method can be regarded as a special case of symmetric alternating direction method. The numerical validity of the symmetric alternating direction method with large step size factor is illustrated by experiments.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O221
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本文编号：1512844