An efficient alternating direction method of multipliers for optimal control problems constrained by random Helmholtz equations

发布时间：2018-04-13 作者：浏览次数：

Speaker:	张凯	DateTime:	2018年4月17日（周二）上午10:30-11:30
Brief Introduction to Speaker: 张凯，吉林大学教授。		Place:	六号楼二楼报告厅
Abstract:Based on the alternating direction method of multipliers (ADMM), we develop three numerical algorithms incrementally for solving the optimal control problems constrained by random Helmholtz equations. First, we apply the standard Monte Carlo technique and finite element method for the random and spatial discretization, respectively, and then ADMM is used to solve the resulting system. Next, combining the multi-modes expansion, Monte Carlo technique, finite element method, and ADMM, we propose the second algorithm. In the third algorithm, we preprocess certain quantities before the ADMM iteration, so that nearly no random variable is in the inner iteration. This algorithm is the most efficient one and is easy to implement. The error estimates of these three algorithms are established. The numerical experiments verify the efficiency of our algorithms.