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
相关论文
共 50 条
  • [41] A Semismooth Newton Multigrid Method for Constrained Elliptic Optimal Control Problems
    Liu, Jun
    Huang, Tingwen
    Xiao, Mingqing
    ADVANCES IN GLOBAL OPTIMIZATION, 2015, 95 : 397 - 405
  • [42] An augmented Lagrange method for elliptic state constrained optimal control problems
    Karl, Veronika
    Wachsmuth, Daniel
    COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2018, 69 (03) : 857 - 880
  • [43] An augmented Lagrange method for elliptic state constrained optimal control problems
    Veronika Karl
    Daniel Wachsmuth
    Computational Optimization and Applications, 2018, 69 : 857 - 880
  • [44] Parallel Algorithms for Constrained Tensor Factorization via Alternating Direction Method of Multipliers
    Liavas, Athanasios P.
    Sidiropoulos, Nicholas D.
    IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2015, 63 (20) : 5450 - 5463
  • [45] An Alternating Direction Method of Multipliers for the Optimization Problem Constrained with a Stationary Maxwell System
    Hao, Yongle
    Song, Haiming
    Wang, Xiaoshen
    Zhang, Kai
    COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2018, 24 (05) : 1435 - 1454
  • [46] Distributed Alternating Direction Method of Multipliers for Linearly Constrained Optimization Over a Network
    Carli, Raffaele
    Dotoli, Mariagrazia
    IEEE CONTROL SYSTEMS LETTERS, 2020, 4 (01): : 247 - 252
  • [47] A Homotopy Alternating Direction Method of Multipliers for Linearly Constrained Separable Convex Optimization
    Yang J.
    Dai Y.-Q.
    Peng Z.
    Zhuang J.-P.
    Zhu W.-X.
    Journal of the Operations Research Society of China, 2017, 5 (2) : 271 - 290
  • [48] An Inertial Alternating Direction Method of Multipliers
    Bot, Radu Ioan
    Csetnek, Ernoe Robert
    MINIMAX THEORY AND ITS APPLICATIONS, 2016, 1 (01): : 29 - 49
  • [49] Parallel alternating direction method of multipliers
    Yan, Jiaqi
    Guo, Fanghong
    Wen, Changyun
    Li, Guoqi
    INFORMATION SCIENCES, 2020, 507 : 185 - 196
  • [50] Distributed Alternating Direction Method of Multipliers
    Wei, Ermin
    Ozdaglar, Asuman
    2012 IEEE 51ST ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2012, : 5445 - 5450
12345