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A dynamical method for optimal control of the obstacle problem

  • Qinghua Ran EMAIL logo , Xiaoliang Cheng , Rongfang Gong and Ye Zhang
Published/Copyright: May 31, 2023

Abstract

In this paper, we consider the numerical method for an optimal control problem governed by an obstacle problem. An approximate optimization problem is proposed by regularizing the original non-differentiable constrained problem with a simple method. The connection between the two formulations is established through some convergence results. A sufficient condition is derived to decide whether a solution of the first-order optimality system is a global minimum. The method with a second-order in time dissipative system is developed to solve the optimality system numerically. Several numerical examples are reported to show the effectiveness of the proposed method.

MSC 2010: 35J86; 49J20; 65K15; 49M05; 70G60

Funding source: Guizhou University

Award Identifier / Grant number: X2022103

Award Identifier / Grant number: 12071215

Award Identifier / Grant number: 12171036

Award Identifier / Grant number: Z210001

Award Identifier / Grant number: 2022YFC3310300

Funding statement: This work was supported by the scientific research project of introducing talents of Guizhou University (No. X2022103), National Natural Science Foundation of China (No. 12071215), National Key Research and Development Program of China (No. 2022YFC3310300), Beijing Natural Science Foundation (No. Z210001) and National Natural Science Foundation of China (No. 12171036).

Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.

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Received: 2020-10-12
Revised: 2022-10-01
Accepted: 2023-02-03
Published Online: 2023-05-31
Published in Print: 2023-08-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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