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

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成果类型:
期刊论文
作者:
Yang, Jinda;Zhang, Kai;Song, Haiming*;Cheng, Ting
通讯作者:
Song, Haiming
作者机构:
[Song, Haiming; Zhang, Kai; Yang, Jinda] Jilin Univ, Dept Math, Changchun 130012, Jilin, Peoples R China.
[Cheng, Ting] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
[Cheng, Ting] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
通讯机构:
[Song, Haiming] J
Jilin Univ, Dept Math, Changchun 130012, Jilin, Peoples R China.
语种:
英文
关键词:
Global Science Press;AAMM;Advances in Applied Mathematics and Mechanics;Optimal control problem;elliptic equation;finite element method;ADMM.
期刊:
应用数学与力学进展
ISSN:
2070-0733
年:
2020
卷:
12
期:
2
页码:
336-361
基金类别:
The work of K. Zhang was supported by the NSF of China under the grant Nos. 11871245, 11771179, 11726102 and by the Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University (No. 93K172018Z01). The work of H. Song was supported by the NSF of China under the grant No. 11701210, the Education Department Project of Jilin Province under the grant No. JJKH20180113KJ, the Science and Technology Department Project of Jilin Province under the grant No. 20190103029JH, and the special funds for basic scientific research operating expenses of central universities. They also wish to thank the high performance computing center of Jilin university and computing center of Jilin province for essential computing support.
机构署名:
本校为其他机构
院系归属:
数学与统计学学院
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 simu...

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