Alternating direction based method for optimal control problem constrained by Stokes equation

Gao，Yu3; Li，Jingzhi1; Song，Yongcun4; Wang，Chao5; Zhang，Kai2

2021

10.1515/jiip-2020-0101

Journal of Inverse and Ill-Posed Problems   影响因子和分区

0928-0219

1569-3945

We consider the optimal control problems constrained by Stokes equations. It has been shown in the literature, the problem can be discretized by the finite element method to generate a discrete system, and the error estimate has also been established. In this paper, we focus on solving the discrete system by the alternating splitting augmented Lagrangian method, which is a direct extension of alternating direction method of multipliers and possesses a global O (1 / k) convergence rate. In addition, we propose an acceleration scheme based on the alternating splitting augmented Lagrangian method to improve the efficiency of the algorithm. The error estimates and convergence analysis of our algorithms are presented for several different types of optimization problems. Finally, numerical experiments are performed to verify the efficiency of the algorithms.

alternating direction based method finite element method optimal control problem Stokes equation

EI ; SCI

英语

通讯

NSF of China[11871245] ; Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University[93K172018Z01]

Mathematics

Mathematics, Applied ; Mathematics

WOS:000891639900005

WALTER DE GRUYTER GMBH

20210309789868

Constrained optimization ; Efficiency ; Navier Stokes equations ; Optimal control systems

Control Systems:731.1 ; Production Engineering:913.1 ; Calculus:921.2 ; Systems Science:961

2-s2.0-85099341818

Scopus

1.Department of Mathematics,South University of Science and Technology of China,Shenzhen,518055,China
2.Department of Mathematics,Jilin University,Changchun,130012,China
3.Department of Mathematics,Jilin University,Changchun,130012,China
4.Department of Mathematics,University of Hong Kong,Hongkong,Hong Kong
5.Department of Mathematics,South University of Science and Technology of China,Shenzhen,518055,China

Gao，Yu,Li，Jingzhi,Song，Yongcun,et al. Alternating direction based method for optimal control problem constrained by Stokes equation[J]. Journal of Inverse and Ill-Posed Problems,2021,30(1):81-99.

Gao，Yu,Li，Jingzhi,Song，Yongcun,Wang，Chao,&Zhang，Kai.(2021).Alternating direction based method for optimal control problem constrained by Stokes equation.Journal of Inverse and Ill-Posed Problems,30(1),81-99.

Gao，Yu,et al."Alternating direction based method for optimal control problem constrained by Stokes equation".Journal of Inverse and Ill-Posed Problems 30.1(2021):81-99.