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

  • Yu Gao , Jingzhi Li EMAIL logo , Yongcun Song , Chao Wang and Kai Zhang EMAIL logo
Published/Copyright: January 5, 2020

Abstract

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.

MSC 2010: 90C30; 90C33; 65N30

Dedicated to Professor Michael Klibanov on the occasion of his 70th birthday


Award Identifier / Grant number: 11871245

Funding source: Jilin University

Award Identifier / Grant number: 93K172018Z01

Funding statement: The work of K. Zhang was supported by the NSF of China under the grant No. 11871245, and by the Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University (93K172018Z01).

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Received: 2020-08-09
Accepted: 2020-11-11
Published Online: 2020-01-05
Published in Print: 2022-02-01

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