An Alternating Direction Method of Multipliers for the Optimization Problem Constrained with a Stationary Maxwell System
An Alternating Direction Method of Multipliers for the Optimization Problem Constrained with a Stationary Maxwell System
复制标题
DOI：
10.4208/cicp.oa-2017-0117
复制
发表时间：
2018
影响因子：
3.7
通讯作者：
Yongle Hao;Haiming Song;Xiaoshen Wang;Kai Zhang
中科院分区：
文献类型：
--
作者：
Yongle Hao;Haiming Song;Xiaoshen Wang;Kai Zhang
本文主要研究一种求解定常Maxwell系统约束最优化问题的有效数值方法。借鉴文献[32]的思想，利用边缘元逼近状态变量和控制变量，将连续最优控制问题离散为有限维问题。本文的创新之处在于离散化系统的求解方法。基于可分离结构，提出了一种交替方向乘法器(ADMM)。进一步，以目标函数误差的形式建立了全局收敛分析，其中包括边缘单元的离散化误差和ADMM的迭代误差。最后，通过数值仿真验证了该算法的有效性。AMS科目分类：90C30、90C33、65K10、65M60
This paper mainly focuses on an efficient numerical method for the optimization problem constrained with a stationary Maxwell system. Following the idea of [32], the edge element is applied to approximate the state variable and the control variable, then the continuous optimal control problem is discretized into a finite dimensional one. The novelty of this paper is the approach for solving the discretized system. Based on the separable structure, an alternating direction method of multipliers (ADMM) is proposed. Furthermore, the global convergence analysis is established in the form of the objective function error, which includes the discretization error by the edge element and the iterative error by ADMM. Finally, numerical simulations are presented to demonstrate the efficiency of the proposed algorithm. AMS subject classifications: 90C30, 90C33, 65K10, 65M60