An Alternating Direction Method of Multipliers for Optimal Control Problems Constrained with Elliptic Equations
Year: 2020
Author: Jinda Yang, Kai Zhang, Haiming Song, Ting Cheng
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0198
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 336–361
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Optimal control problem elliptic equation finite element method ADMM.