An Alternating Direction Method of Multipliers for Optimal Control Problems Constrained with Elliptic Equations

被引：2
|
作者：
Yang, Jinda [1 ]
Zhang, Kai [1 ]
Song, Haiming [1 ]
Cheng, Ting [2 ,3 ]
机构：
[1] Jilin Univ, Dept Math, Changchun 130012, Jilin, Peoples R China
[2] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China
[3] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2020年 / 12卷 / 02期
关键词：
Optimal control problem; elliptic equation; finite element method; ADMM; VARIATIONAL-INEQUALITIES; NUMERICAL APPROXIMATION; CONVERGENCE RATE; NEWTON METHODS; PROJECTION; REGULARITY;
D O I：
10.4208/aamm.OA-2018-0198
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we propose an efficient numerical method for the optimal control problem constrained by elliptic equations. Being approximated by the finite element method (FEM), the continuous optimal control problem is discretized into a finite dimensional optimization problem with separable structures. Furthermore, an alternating direction method of multipliers (ADMM) is applied to solve the discretization problem. The total convergence analysis which includes the discretization error by FEM and iterative error by ADMM is established. Finally, numerical simulations are presented to verify the efficiency of the proposed method.
引用
收藏
页码：336 / 361
页数：26
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