Volume 12, Issue 2
An Alternating Direction Method of Multipliers for Optimal Control Problems Constrained with Elliptic Equations

Adv. Appl. Math. Mech., 12 (2020), pp. 336-361.

Published online: 2020-01

Cited by

Export citation
• Abstract

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.

49M37, 65K10, 65M60, 90C33

kzhang@jlu.edu.cn (Kai Zhang)

songhaiming@jlu.edu.cn (Haiming Song)

• BibTex
• RIS
• TXT
@Article{AAMM-12-336, author = {Yang , JindaZhang , KaiSong , Haiming and Cheng , Ting}, title = {An Alternating Direction Method of Multipliers for Optimal Control Problems Constrained with Elliptic Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {2}, pages = {336--361}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0198}, url = {http://global-sci.org/intro/article_detail/aamm/13625.html} }
TY - JOUR T1 - An Alternating Direction Method of Multipliers for Optimal Control Problems Constrained with Elliptic Equations AU - Yang , Jinda AU - Zhang , Kai AU - Song , Haiming AU - Cheng , Ting JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 336 EP - 361 PY - 2020 DA - 2020/01 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2018-0198 UR - https://global-sci.org/intro/article_detail/aamm/13625.html KW - Optimal control problem, elliptic equation, finite element method, ADMM. AB -

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.

Jinda Yang, Kai Zhang, Haiming Song & Ting Cheng. (2020). An Alternating Direction Method of Multipliers for Optimal Control Problems Constrained with Elliptic Equations. Advances in Applied Mathematics and Mechanics. 12 (2). 336-361. doi:10.4208/aamm.OA-2018-0198
Copy to clipboard
The citation has been copied to your clipboard