An alternating direction method of multipliers for elliptic equation constrained optimization problem

详细信息    查看全文

• 作者：Kai Zhang ; JingShi Li ; YongCun Song ; XiaoShen Wang
• 关键词：ADMM ; optimal control problems ; elliptic equation constrained
• 刊名：Science China Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：60
• 期：2
• 页码：361-378
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics;
• 出版者：Science China Press
• ISSN：1869-1862
• 卷排序：60

文摘

We propose an alternating direction method of multipliers (ADMM) for solving the state constrained optimization problems governed by elliptic equations. The unconstrained as well as box-constrained cases of the Dirichlet boundary control, Robin boundary control, and right-hand side control problems are considered here. These continuous optimization problems are transformed into discrete optimization problems by the finite element method discretization, then are solved by ADMM. The ADMM is an efficient first order algorithm with global convergence, which combines the decomposability of dual ascent with the superior convergence properties of the method of multipliers. We shall present exhaustive convergence analysis of ADMM for these different type optimization problems. The numerical experiments are performed to verify the efficiency of the method.