带有邻近点项交替方向乘子法的双乘子步长更新研究
发布时间：2019-03-11 14:05
【摘要】：对称的交替方向乘子法(ADMM)是Peaceman-Rachford分裂方法的一个应用。原始的对称交替方向乘子法是经验性的,理论上并不能保证它的收敛性。最近,何炳生等人(2016)在对称的交替方向乘子法中采用不同的步长来更新乘子,并证明了它的收敛性。他们使用Glowinski的大步长来更新拉格朗日乘子,使得此方法变得更加灵活。在本文中,我们在其更新初始变量的子问题中增加了半正定的邻近点项,得到了仍然能够使用Glowinski的大步长来更新拉格朗日乘子的结论。我们证明了带有邻近点项的交替方向乘子法的收敛性和在遍历意义下具有O(1/t)的收敛率。最后,我们用数值实验说明了选择大步长的优势和该方法的有效性。
[Abstract]:The symmetric alternating direction multiplier method (ADMM) is an application of the Peaceman-Rachford splitting method. The original symmetric alternating direction multiplier method is empirical and cannot guarantee its convergence theoretically. Recently, he Bingsheng et al. (2016) used different steps to update multipliers in symmetric alternating direction multiplier method, and proved its convergence. They used the big steps of Glowinski to update Lagrangian multipliers, making the approach more flexible. In this paper, we add semi-definite neighbor term to the sub-problem of updating initial variable, and obtain the conclusion that we can still update Lagrangian multipliers by using the large step length of Glowinski. We prove the convergence of the alternating direction multiplier method with adjacent point term and the convergence rate of O (1) in the sense of ergodic. Finally, numerical experiments are used to illustrate the advantages of large step selection and the effectiveness of this method.
【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】：O224
，
本文编号：2438341
[Abstract]:The symmetric alternating direction multiplier method (ADMM) is an application of the Peaceman-Rachford splitting method. The original symmetric alternating direction multiplier method is empirical and cannot guarantee its convergence theoretically. Recently, he Bingsheng et al. (2016) used different steps to update multipliers in symmetric alternating direction multiplier method, and proved its convergence. They used the big steps of Glowinski to update Lagrangian multipliers, making the approach more flexible. In this paper, we add semi-definite neighbor term to the sub-problem of updating initial variable, and obtain the conclusion that we can still update Lagrangian multipliers by using the large step length of Glowinski. We prove the convergence of the alternating direction multiplier method with adjacent point term and the convergence rate of O (1) in the sense of ergodic. Finally, numerical experiments are used to illustrate the advantages of large step selection and the effectiveness of this method.
【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】：O224
，
本文编号：2438341
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